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Compute 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

Compute 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 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 a standard deviation of 5.6. Who did better on their test in their respective classes.

5. Given Z is a standar 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 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).

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