Exam 9: The Normal Distribution

When considering area under the standard normal curve, decide whether the area to the left of $z=2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

(Multiple Choice)

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Question 61

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated. -Between $1 / 2$ and $3 / 2$

(Short Answer)

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Question 62

The formula $\mu=n p$ is used to convert any normally distributed variable to one which has a mean of 0 and a standard deviation of 1.

(True/False)

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Question 63

When considering area under the standard normal curve, decide whether the area to the left of $z=-2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

(Multiple Choice)

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Question 64

The normal approximation to the binomial distribution applies in problems that originally involve the normal distribution.

(True/False)

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Question 65

For the uniform distribution pictured below, the probability $P(x=2)$ equals

(Multiple Choice)

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Question 66

Find $z$ if the normal curve area to the right of $z$ is 0.3483 .

(Short Answer)

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Question 67

Find $z$ if the normal curve area to the right of $z$ is 0.8665 .

(Short Answer)

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Question 68

A salesperson knows that $20 \%$ of her presentations result in sales. Find the probabilities that in the next 60 presentations} -at least 9 result in sales.

(Short Answer)

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Question 69

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=-1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=2$ and $\mathrm{z}=2.5$ .

(Multiple Choice)

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Question 70

Find $z$ if the normal curve area to the left of $z$ is 0.1611 .

(Short Answer)

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Question 71

Find $z$ if the normal curve area to the right of $z$ is 0.8997 .

(Short Answer)

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Question 72

The mean of every normal distribution is equal to 0.

(True/False)

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Question 73

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time -between 55 and 59 products, inclusive, will be successful.

(Short Answer)

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Question 74

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. -Find the probability that a customer spends less than 48 minutes in the supermarket.

(Short Answer)

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Question 75

Find the indicated normal-curve area using the normal table. -Between $z=-2$ and $z=-1$ .

(Short Answer)

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Question 76

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. -Find the probability that between 15 and 18 ounces are dispensed in a cup.

(Short Answer)

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Question 77

Find the indicated normal-curve area using the normal table. -Between $\mathrm{z}=-1.23$ and $\mathrm{z}=1.23$

(Short Answer)

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Question 78

The $z$ value such that $50 \%$ of the area is to the right of $z$ is _______.

(Short Answer)

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Question 79

The standard normal distribution has a mean of _ and a standard deviation of _.

(Short Answer)

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Question 80

When considering area under the standard normal curve, decide whether the area to the left of $z=2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated. -Between $1 / 2$ and $3 / 2$

The formula $\mu=n p$ is used to convert any normally distributed variable to one which has a mean of 0 and a standard deviation of 1.

When considering area under the standard normal curve, decide whether the area to the left of $z=-2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

The normal approximation to the binomial distribution applies in problems that originally involve the normal distribution.

For the uniform distribution pictured below, the probability $P(x=2)$ equals

Find $z$ if the normal curve area to the right of $z$ is 0.3483 .

Find $z$ if the normal curve area to the right of $z$ is 0.8665 .

A salesperson knows that $20 \%$ of her presentations result in sales. Find the probabilities that in the next 60 presentations} -at least 9 result in sales.

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=-1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=2$ and $\mathrm{z}=2.5$ .

Find $z$ if the normal curve area to the left of $z$ is 0.1611 .

Find $z$ if the normal curve area to the right of $z$ is 0.8997 .

The mean of every normal distribution is equal to 0.

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time -between 55 and 59 products, inclusive, will be successful.

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. -Find the probability that a customer spends less than 48 minutes in the supermarket.

Find the indicated normal-curve area using the normal table. -Between $z=-2$ and $z=-1$ .

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. -Find the probability that between 15 and 18 ounces are dispensed in a cup.

Find the indicated normal-curve area using the normal table. -Between $\mathrm{z}=-1.23$ and $\mathrm{z}=1.23$

The $z$ value such that $50 \%$ of the area is to the right of $z$ is _______.

The standard normal distribution has a mean of _ and a standard deviation of _.

Introduction

Summarizing Data: Listing and Grouping

Summarizing Data: Measures of Location

Summarizing Data: Measures of Variation

Possibilities and Probabilities

Some Rules of Probability

Expectations and Decisions

Probability Distributions

Sampling and Sampling Distributions

Problems of Estimation

Tests of Hypotheses: Means

Tests of Hypotheses: Standard Deviations

Tests of Hypotheses Based on Count Data

Analysis of Variance

Regression

Correlation

Nonparametric Tests

Filters

Exam 9: The Normal Distribution

When considering area under the standard normal curve, decide whether the area to the left of z=2.5z=2.5z=2.5 is bigger than, smaller than, or equal to the area to the right of z=2.5\mathrm{z}=2.5z=2.5 .

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated. -Between 1/21 / 21/2 and 3/23 / 23/2

The formula μ=np\mu=n pμ=np is used to convert any normally distributed variable to one which has a mean of 0 and a standard deviation of 1.

When considering area under the standard normal curve, decide whether the area to the left of z=−2.5z=-2.5z=−2.5 is bigger than, smaller than, or equal to the area to the right of z=2.5\mathrm{z}=2.5z=2.5 .

The normal approximation to the binomial distribution applies in problems that originally involve the normal distribution.

For the uniform distribution pictured below, the probability P(x=2)P(x=2)P(x=2) equals

Find zzz if the normal curve area to the right of zzz is 0.3483 .

Find zzz if the normal curve area to the right of zzz is 0.8665 .

A salesperson knows that 20%20 \%20% of her presentations result in sales. Find the probabilities that in the next 60 presentations} -at least 9 result in sales.

When considering area under the standard normal curve, decide whether the area between z=−1.5z=-1.5z=−1.5 and z=−1z=-1z=−1 is bigger than, smaller than, or equal to the area between z=2\mathrm{z}=2z=2 and z=2.5\mathrm{z}=2.5z=2.5 .

Find zzz if the normal curve area to the left of zzz is 0.1611 .

Find zzz if the normal curve area to the right of zzz is 0.8997 .

The mean of every normal distribution is equal to 0.

An electronics firm believes that 70%70 \%70% of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time -between 55 and 59 products, inclusive, will be successful.

A supermarket manager has determined that the amount of time customers spend in the supermarket is approximately normally distributed with a mean of 45 minutes and a standard deviation of 6 minutes. -Find the probability that a customer spends less than 48 minutes in the supermarket.

Find the indicated normal-curve area using the normal table. -Between z=−2z=-2z=−2 and z=−1z=-1z=−1 .

The number of ounces of soda that a vending machine dispenses per cup is normally distributed with a mean of 12 ounces and a standard deviation of 4 ounces. -Find the probability that between 15 and 18 ounces are dispensed in a cup.

Find the indicated normal-curve area using the normal table. -Between z=−1.23\mathrm{z}=-1.23z=−1.23 and z=1.23\mathrm{z}=1.23z=1.23

The zzz value such that 50%50 \%50% of the area is to the right of zzz is _______.

The standard normal distribution has a mean of _______ and a standard deviation of _______.

Introduction

Summarizing Data: Listing and Grouping

Summarizing Data: Measures of Location

Summarizing Data: Measures of Variation

Possibilities and Probabilities

Some Rules of Probability

Expectations and Decisions

Probability Distributions

Sampling and Sampling Distributions

Problems of Estimation

Tests of Hypotheses: Means

Tests of Hypotheses: Standard Deviations

Tests of Hypotheses Based on Count Data

Analysis of Variance

Regression

Correlation

Nonparametric Tests

Filters

When considering area under the standard normal curve, decide whether the area to the left of $z=2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

The graph shows the distribution of a continuous random variable that takes on values on the continuous interval from -2 to 2 . Find the probability that this random variable will take on the value indicated. -Between $1 / 2$ and $3 / 2$

The formula $\mu=n p$ is used to convert any normally distributed variable to one which has a mean of 0 and a standard deviation of 1.

When considering area under the standard normal curve, decide whether the area to the left of $z=-2.5$ is bigger than, smaller than, or equal to the area to the right of $\mathrm{z}=2.5$ .

For the uniform distribution pictured below, the probability $P(x=2)$ equals

Find $z$ if the normal curve area to the right of $z$ is 0.3483 .

Find $z$ if the normal curve area to the right of $z$ is 0.8665 .

A salesperson knows that $20 \%$ of her presentations result in sales. Find the probabilities that in the next 60 presentations} -at least 9 result in sales.

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=-1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=2$ and $\mathrm{z}=2.5$ .

Find $z$ if the normal curve area to the left of $z$ is 0.1611 .

Find $z$ if the normal curve area to the right of $z$ is 0.8997 .

An electronics firm believes that $70 \%$ of the new products they market will be successful. If the company markets 80 products in the next 5 years, find the probability that in that time -between 55 and 59 products, inclusive, will be successful.

Find the indicated normal-curve area using the normal table. -Between $z=-2$ and $z=-1$ .

Find the indicated normal-curve area using the normal table. -Between $\mathrm{z}=-1.23$ and $\mathrm{z}=1.23$

The $z$ value such that $50 \%$ of the area is to the right of $z$ is _______.

The standard normal distribution has a mean of _ and a standard deviation of _.