Exam 6: The Normal Distribution

The length of country and western songs is normally distributed and has a mean of seconds and a standard deviation of 30 seconds. Find the probability that a random Selection of 16 songs will have mean length of 181.98 seconds or less. Assume the Distribution of the lengths of the songs is normal.

A normal population has a mean $\mu = 40$ and standard deviation $\sigma = 11$ . What proportion of the population is between 24 and $32 ?$

If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12, find the percentage of scores that will fall below 50.

The mean weight of loads of rock is 51.0 tons with a standard deviation of 10.0 tons. If 36 loads are chosen at random for a weight check, find the probability that the mean Weight of those loads is less than 50.3 tons. Assume that the variable is normally Distributed.

For a normal distribution curve with a mean of 15 and a standard deviation of 5, which range of the variable defines an area under the curve corresponding to a probability of Approximately 68%?

A sample of size 50 will be drawn from a population with mean 76 and standard deviation 14 . Find the 69 th percentile of $\bar { x }$ .

The average length of crocodiles in a swamp is 11.5 feet. If the lengths are normally distributed with a standard deviation of 1.7 feet, find the probability that a crocodile is More than 11 feet long.

The weights of 6-week-old poults (juvenile turkeys) are normally distributed with a mean 8.9 pounds and standard deviation 1.9 pounds. A turkey farmer wants to provide a Money-back guarantee that her 6-week poults will weigh at least a certain amount. What Weight should she guarantee so that she will have to give her customer's money back Only 1% of the time?

As the sample size $n$ increases, the shape of the distribution of the sample means taken with replacement from a population with mean $\mu$ and standard deviation $\sigma$ , will approach a normal distribution. This distribution will have a mean of $\mu$ and a standard deviation of $\frac { \sigma } { \sqrt { n } }$ . This is a statement of the___________

Use the normal approximation to find the indicated probability. The sample size is population proportion of successes is $p$ , and $X$ is the number of successes in the sample. $n = 90 , p = 0.41 : P ( 32 < X < 43 )$

A normal population has a mean $\mu = 28$ and standard deviation $\sigma = 5$ . What proportion of the population is less than 23 ?

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person In Africa is selected at random, what is the probability that the person will die before the Age of 65?

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL. The fill volumes are normally distributed. What Proportion of bottles have volumes between 992 mL and 998 mL?

$X$ is a normally distributed random variable with a mean of $7.0$ and a standard deviation of 3.00. Find the value $x$ such that $P ( X < x )$ is equal to $0.86$ . (Note: the diagram is not necessarily to scale.)

$X$ is a normally distributed random variable with a mean of $11.00$ . If the probability that $X$ is less than $11.88$ is $0.67$ (as shown below), then what is the standard deviation of (Note: the diagram is not necessarily to scale.)

Which choice is another term that can be used to describe a normal distribution:

Find the area under the standard normal distribution curve between $z = - 2.05$ and $z =$ $2.05$ .

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness. 21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

$X$ is a normally distributed random variable with a standard deviation of $2.00$ . Find the mean of $X$ if $12.71 \%$ of the area under the distribution curve lies to the right of $10.28$ . (Note: the diagram is not necessarily to scale.)