If Z is a standard normal variable, find the probability. The probability that Z lies between -0.87 and 2.34

If z is a standard normal variable, find the probability. P(z < 0.97)

Assume that X has a normal distribution, and find the indicated probability. The mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than 53.0.

Solve the problem. Round to the nearest tenth unless indicated otherwise. The amount of rainfall in January in a certain city is normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. Find the value of the quartile Q1.

Find the indicated probability. The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

Which of the sample statistics are unbiased estimators of their population parameters?

A poll of 2000 randomly selected students in grades 6 through 8 was conducted and found that 41% enjoy playing sports. Would confidence in the results increase if the sample size were 3800 instead of 2000? Why or why not?

Solve the problem. The weights of the fish in a certain lake are normally distributed with a mean of 10 lb and a standard deviation of 9. If 9 fish are randomly selected, what is the probability that the mean weight will be between 7.6 and 13.6 lb?

Solve the problem. The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 75 inches, and a standard deviation of 16 inches, What is the probability that the mean annual snowfall during 64 randomly picked years will exceed 77.8 inches?

Find the indicated critical z value. Find the critical value zα/2 that corresponds to a 94% confidence level.

Express the confidence interval using the indicated format. Express the confidence interval -0.035 < p < 0.565 in the form of ± E.

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. In a clinical test with 3500 subjects, 1750 showed improvement from the treatment. Find the margin of error for the 99% confidence interval used to estimate the population proportion.

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.09; confidence level: 90%; from a prior study, is estimated by 0.21.

Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 90%; n = 10; σ is unknown; population appears to be normally distributed.

Use the confidence level and sample data to find the margin of error E. Replacement times for washing machines: 90% confidence; n = 45,  = 119 years, σ = 2.1 years

Provide an appropriate response. The grade point averages for 10 randomly selected junior college students are listed below. Assume the grade point averages are normally distributed. Find a 98% confidence interval for the true mean. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

Use the given information to find the minimum sample size required to estimate an unknown population mean μ. How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confidence that the sample mean is within $2 of the population mean, and the population standard deviation is known to be $89.

Solve the problem. Find the chi-square value χ 2/L corresponding to a sample size of 7 and a confidence level of 99 percent.

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. To find the standard deviation of the diameter of wooden dowels, the manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval for the population standard deviation σ.