Exam 6: The Normal Distribution

Find the specified percentile, quartile, or decile. -The amount of Jen's monthly phone bill is normally distributed with a mean of $54 and a standard deviation of $8. Find the first quartile, $\mathrm { Q } _ { 1 } .$

Use a table of areas to find the specified area under the standard normal curve. -The area that lies to the right of -1.82

Find the indicated probability or percentage for the normally distributed variable. -The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days?

Use the empirical rule to solve the problem. -The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a Systolic blood pressure that lies within 3 standard deviations to either side of the mean?

Solve the problem. -Frequency data were reported for the ages of women who became mothers during one year in a selected U.S. city. The age distribution is given in the table. Obtain a relative-frequency histogram Of these data and determine whether the ages are approximately normally distributed. Age (yrs) Frequency 15-under 20 101 20-under 25 270 25-under 30 285 30 -under 35 479 35 -under 40 867 40 -under 45 1021 45 -under 50 225 50 -under 55 56

Find the specified percentile, quartile, or decile. -Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the value of the third quartile.

In assessing the normality of data, why is a normal probability plot especially advantageous for small samples?

Use the empirical rule to solve the problem. -The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 400 hours and a standard deviation of 12 hours. What percentage of the bulbs have lifetimes that lie within 2 Standard deviations to either side of the mean?

Use the empirical rule to solve the problem. -The annual precipitation for one city is normally distributed with a mean of 35.6 inches and a standard deviation of 2.9 inches. Fill in the blanks. In 99.74% of the years, the precipitation in this city is between ___ and ___ inches.

Sketch a standard normal curve and shade the area to the right of the z-score 1.6.

A normal probability plot is given below for the lifetimes (in hours)of batteries of a particular type. Use the plot to identify outliers, if any. Explain your reasoning.

Use a table of areas for the standard normal curve to find the required z-score. -Find the z-score for which the area under the standard normal curve to its left is 0.96

Use a table of areas to find the specified area under the standard normal curve. -The area that lies either to the left of -2.61 or to the right of 0.66

Find the indicated probability or percentage for the normally distributed variable. -The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter Greater than 0.32 inches?

Solve the problem. -Data were reported for household size (number of people in household)in a small community. The size distribution is given in the table. Obtain a relative-frequency histogram for these data and Determine whether the household sizes are approximately normally distributed. Size (\# of people) Frequency 1-under 2 4 2-under 3 0 3-under 4 2 4-under 5 10 5-under 6 32 6-under 7 28 7-under 8 8 8-under 9 4

Find the indicated probability or percentage for the normally distributed variable. -The variable $X$ is normally distributed. The mean is $\mu = 15.2$ and the standard deviation is $\sigma = 0.9$ . Find $P ( X > 16.1 )$ .

Use a table of areas for the standard normal curve to find the required z-score. -Find the z-score for having area 0.07 to its right under the standard normal curve, that is, find ${ } ^ { \mathrm { z } } 0.07 ^ { \mathrm { . } }$

How does the standard normal distribution differ from a nonstandard normal distribution? Why is it necessary to standardize in order to find percentages for nonstandard normal variables?

Use a table of areas for the standard normal curve to find the required z-score. -Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.

Use the empirical rule to solve the problem. -The amount of Jen's monthly phone bill is normally distributed with a mean of $73 and a standard deviation of $9. What percentage of her phone bills are between $46 and $100?