A normal population has a mean of 75 and a standard deviation of 5. You choose a 40-person sample. Calculate the likelihood that the sample mean is less than 74.

A normal population has a mean of $75$ and a standard deviation of $5$. You select a random sample of $40$. Compute the probability the sample mean of between $74$ and $76$.

A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40. Compute the probability the sample mean is: a. Less than 74. b. Between 74 and 76. c. Between 76 and 77. d. Greater than 77

Sketch a normal curve with a mean of 75 and a standard deviation of 10 and a normal curve with a mean of 75 and a standard deviation of 5. Which curve displays less variability?

The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of$250 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 50 one bedroom apartments and finding the mean to be at least $1,950 per month?

A random sample of size $n=200$ is taken from a population with a population proportion $p=$ $0.75$.

a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion.

b. What is the probability that the sample proportion is between $0.70$ and $0.80$ ?

c. What is the probability that the sample proportion is less than $0.70$ ? Applications

The mean in a normal population is 60, and the standard deviation is 12. You choose nine at random. Calculate the probability that the sample mean is between 56 and 63

The mean in a normal population is 60, and the standard deviation is 12. You choose nine at random. Calculate the probability that the sample mean is greater than 63.

The mean in a normal population is 60, and the standard deviation is 12. You choose nine at random. Calculate the probability that the sample mean is less than 56

Suppose the U.S. president wants an estimate of the proportion of the population who support his current policy toward revisions in the health care system. The president wants the estimate to be within .04 of the true proportion. Assume a 95 percent level of confidence. The president’s political advisors estimated the proportion supporting the current policy to be .60. a. How large of a sample is required? b. How large of a sample would be necessary if no estimate were available for the proportion supporting current policy?

A random sample of size n=50 is selected from a binomial distribution with population proportion p=.7. a. What will be the approximate shape of the sampling distribution of $\hat{p}$? b. What will be the mean and standard deviation (or standard error) of the sampling distribution of $\hat{p}$? c. Find the probability that the sample proportion $\hat{p}$ is less than .8.

When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 92.0 and a standard deviation of 3.6. A random sample of 4 different hours was taken.

Find the mean of the sampling distribution of the sample means.

Find the variance of the sampling distribution of the sample mean.

Find the standard error of the sampling distribution of the sample mean.

What is the probability that the sample mean exceeds 93.0 units?

In the law firm Tybo and Associates, there are six partners. Listed is the number of cases each partner actually tried in court last month.

$$\begin{array}{|lc|} \hline \text { Partner } & \text { Number of Cases } \\ \hline \text { Ruud } & 3 \\ \text { Wu } & 6 \\ \text { Sass } & 3 \\ \text { Flores } & 3 \\ \text { Wilhelms } & 0 \\ \text { Schueller } & 1 \end{array}$$

a. How many different samples of size 3 are possible? b. List all possible samples of size 3 , and compute the mean number of cases in each sample. c. Compare the mean of the distribution of sample means to the population mean. d. On a chart similar to Chart $8-2$, compare the dispersion in the population with that of the sample means.

A population consists of the following five values: 12, 12, 14, 15, and 20. a. List all samples of size 3, and compute the mean of each sample. b. Compute the mean of the distribution of sample means and the population mean. Compare the two values. c. Compare the dispersion in the population with that of the sample means