Compute the z-score. Round your answer to two decimal places.

1. Given X~N (69, 3.1), find z-score when x = 69

Solve the problem

2. Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(-a < z < a) = 0.8686. Find a. State your answer to two decimal places.

3. Suppose X~N(192, 52) represents online purchases by residents in New York, and Y~N(204, 56) represents online purchases by residents in Arizona. Bill is a resident in New York, and he spends on average $204 online. Melissa lives in Arizona, and she spends on average $212 online. Compute z-score for Bill and Melissa. State your answer to two decimal places.

4. Two friends, Steve and Natalie, took a midterm exam in a Chemistry class from the same instructor but during different semesters. Steve scored 85 points on the exam with the class mean of 78 and standard deviation of 5.2 points. Natalie scored 89 points with the class mean of 83 and standard deviation of 5.6 Who did better on their test in their respective classes.

5. Given Z is a standard normal variable, find the area under the bell curve to the right of Z-value of 1.42. State your answer to four decimal places.

6. The mean weight of a can of soda is 17.5 oz with standard deviation of 0.3 oz. Use the Empirical Rule to estimate the probability that the weight of randomly selected can of soda is between 16.9 and 18.1 ounces; that is P(16.9 < X < 18.1).

If Z is a standard normal variable, find the probability.

7. The probability that Z lies between -0.55 and 0.55

8. P(Z < 0.97)

Compute standard deviation.

9. An unknown distribution has a mean of 160 and standard deviation of 29. Samples of the size 32 are randomly drawn from the population. Compute standard deviation of the sampling distribution. Round your answer to two decimal places.

Compute probability.

10. An unknown distribution has a mean of 192 and standard deviation of 38. Samples of the size 42 are randomly drawn from the population. Find the probability that the sample mean is greater than 187. Round your answer to four decimal places.

11. An unknown distribution has a mean of 668 and standard deviation of 96. Samples of the size 32 are randomly drawn from the population. Find the probability that the sample mean is between 649 and 688. Round your final answer to four decimal places. When solving the problem, round your sample standard deviation to one decimal place.

Compute z-score. Round your answer to two decimal places.

12. An unknown distribution has a mean of 122 and standard deviation of 18. A sample size of 46 is randomly drawn from the population. Find z-score for the sum of the samples of 5778. Round your answer to two decimal places.

Compute probability.

13. An unknown distribution has a mean of 62 and standard deviation of 11. A sample size of 47 is randomly drawn from the population, Compute probability that the sum of the samples is less than 2,849. Round your answer to four decimal places.

14. An unknown distribution has a mean of 28 and standard deviation of 4.2. A sample size of 72 is randomly drawn from the population. Compute probability that the sum of the samples is between 1,944 and 2,048. Round your answer to four decimal places.

Solve the problem.

15. An unknown distribution has a mean of 80 and a standard deviation of 12. A sample size of 95 is drawn randomly from the population. Find the sum that is two standard deviations above the mean of the sums. State your answer to two decimal places.