Exam 9: The Normal Distribution

The waiting time in a doctor's office has an exponential distribution with $\mu=45$ minutes. Find the probability that -a patient has to wait between 35 and 50 minutes.

The binomial distribution can be approximated by the normal distribution when _______ and _______.

Find the standard normal-curve area indicated using the normal table. -To the left of $z=-0.54$

If a random variable has the normal distribution with $\mu=30$ and $\sigma=5$ , find the probability that it will take on the indicated value. -Between 24 and 28

If $x$ is a normal random variable with $\mu=50$ and $\sigma=6$ , then the probability that $x$ is not between 44 and 56 is

The annual number of earthquakes in a certain region is a random variable having approximately a normal distribution with $\mu=15.7$ . What is the standard deviation of this distribution if the probability is 0.70 that there will be at least 14 earthquakes? Round answer to the nearest tenth.

Find the following $z$ values. -45}\)

The equation $f(x)=0.125$ can serve as the probability density function of a random variable that takes on values on the interval from 1 to 8 .

It is never desirable to use the normal approximation to the binomial distribution to solve binomial problems that can be solved by using Table V.

Find the standard normal-curve area indicated using the normal table. -Between $\mathrm{z}=-1.3$ and $\mathrm{z}=-0.4$

It has been estimated that $40 \%$ of the televisions that a manufacturer makes need repairs in the first three years of operation. A new hotel buys 90 televisions from this company. Find the probability that in the first three years of operation -between 38 and 42 of the televisions, inclusive, need repairs.

The probability of obtaining exactly 20 successes in 50 trials

If a normal distribution has $\mu=40$ and $\sigma=5$ , the area to the left of $x=42$ equals _______.

The problem that is solved by using the standard formula table and the formula $\mu=n p$

If $x$ is a normal random variable, the probability that $x$ is exactly equal to any number is _______.

A normal distribution has mean $\mu=60$ . If $15.87 \%$ of the area under the curve is to the left of 54 , find the area between 58 and 63 .

Find $z$ if the normal curve area between 0 and $z$ is 0.4345 .

When considering area under the standard normal curve, decide whether the area between $z=-1.5$ and $z=1.1$ is bigger than, smaller than, or equal to the area between $\mathrm{z}=-1.1$ and $\mathrm{z}=1.5$ .

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 and 1

A machine pours beer into $16 \mathrm{oz}$ . bottles. Experience has shown that the number of ounces poured is normally distributed with a standard deviation of 1.5 ounces. Find the probabilities that the amount of beer the machine will pour into the next bottle will be -more than 17 ounces.