# Normal probability

1) The manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.

a. What is the probability that a randomly selected ball bearing will be acceptable ? (Round to tenth of a percent)

b. What does the acceptable range of the diameter need to be if you wanted to accept 98% of the ball bearings ? (Round to thousandths)

2) A final exam in Sociology has a mean of 72 and a standard deviation of 9.2. If 35 students are randomly selected, find the probability that that the mean of their test scores will be greater than 76. (Round to tenth of a percent)

3) In a preliminary study, the sample standard deviation for the duration of a particular back pain suffered by patients was 18.0 months. How large a random sample is needed to construct a 90% confidence interval so that an estimate can be made within 2 months of the actual duration ?

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#### Solution Summary

The solution provides step by step method for the calculation of probability using Z score. Formula for the calculation and Interpretations of the results are also included.