Question 1

For a standard normal distribution, find:

P(z

Find c rounded to two decimal places.

Question 2

The annual rainfall in a certain region is approximately normally distributed with mean 42.7 inches and standard deviation 5.5 inches. Round answers to the nearest tenth of a percent.

a) What percentage of years will have an annual rainfall of less than 44 inches?_____%

b) What percentage of years will have an annual rainfall of more than 39 inches?_____%

c) What percentage of years will have an annual rainfall of between 37 inches and 43 inches?_____%

Question 3

A variable is normally distributed with mean 17 and standard deviation 3. Use your graphing calculator to find each of the following areas. Write your answers in decimal form. Round to the nearest thousandth as needed.

a) Find the area to the left of 19._____

b) Find the area to the left of 11._____

c) Find the area to the right of 16._____

d) Find the area to the right of 20._____

e) Find the area between 11 and 27._____

Question 4

z = 3 is what percentile?

=________percentile

State your answer to the nearest tenth of a percent.

Question 5

Noelle and Ashley began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Noelle took a test in Science and earned a 79.4, and Ashley took a test in English and earned a 67.5. Use the fact that all the students' test grades in the Science class had a mean of 75.1 and a standard deviation of 11.5, and all the students' test grades in English had a mean of 66.9 and a standard deviation of 10.6 to answer the following questions.

a)Calculate the z-score for Noelle's test grade.

z=

b)Calculate the z-score for Ashley's test grade.

z=

c)Which person did relatively better?

• Noelle
• Ashley
• They did equally well.

Question 6

A population of values has an unknown distribution with =93.3and=65.8. You intend to draw a random sample of sizen=39.

What is the mean of the distribution of sample means?

xbar= _____ (Please enter an exact answer.)

What is the standard deviation of the distribution of sample means?

xbar= _____ (Please report your answer accurate to 2 decimal places.)

Question 7

A population of values has a normal distribution with=271.8 and=4.6. You intend to draw a random sample of sizen=10. Roundz

to two (2) decimal places and final answer to 4 decimal places.

Find the probability that a single randomly selected value is less than 275.

P(x

Find the probability that a sample of sizen=10is randomly selected with a mean less than 275.

P(xbar

Question 8

For a confidence level of 90%, find the criticalzvalue. Round to at least 2 decimal places.

Critical z = _____

Question 9

The table below contains the birth weights in grams of 26 African American babies born at BayState Medical Center in Springfield, Massachusetts in 1986. Compute a 95% confidence interval for birth weight.

Directions:Click on the Data button below to display the data. Copy the data into a statistical software package and click the Data button a second time to hide it.

Weight

2531

2771

2918

2930

2938

2964

2977

3062

3060

3297

3369

3428

3486

3757

3847

1153

1735

1957

2090

2218

2278

2382

2403

2388

2473

2501

1. Find the point estimate for the birth weights. Round your answer to 2 decimal places.
2. Determine the value oftc. Round your answer to 5 decimal places.
3. Find the margin of error for the confidence interval. Round your answer to 1 decimal place.
4. Construct the confidence interval for birth weights. Enter your answer as an open interval of the form (a,b) and round to the nearest integer.
5. Babies weighing less than 2500 grams are considered to be of low birth weight. Can you conclude that the average birth weight is greater than 2500 grams?

• Yes, the entire confidence is above2500.
• No conclusions can be drawn since the confidence interval contains2500
• No, the entire confidence interval is below2500

Question 10

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately=44.2. You would like to be 95% confident that your esimate is within 10.5 of the true population mean. How large of a sample size is required?

n=_____

Do not round mid-calculation. However, use acritical z value accurate to two (2) decimal places.