A random number generator on a calculator yields numbers between 0 and 1. the nu

Question

A random number generator on a calculator yields numbers between 0 and 1. the numbers are uniformly distributed with a mean of 0.5 and a standard deviation of 0.289. If 100 numbers are generated, find: A. The probability that their mean is greater than 0.57. B. Would generating 100 numbers with a mean of 0.57 be unusual? If so, why? 1. A random number generator on a calculator yields numbers between 0 and 1. The numbers are uniformly distributed with a mean of .5 and a standard deviation of .289. 100 numbers are generated, find: a. The probability that their mean is greater than .57 b. Would generating 100 numbers with a mean of .57 be unusual? lfso, why? 2. Estimate the probability of getting at least 65 girls in 100 births. If applicable, use the normal distribution to find your answer (Do not forget to use the continuity correction if you can use the normal distribution.). Assume boys and girls are equally likely. (b) would having 65 girls born in 100 births be unusual? Why or why not? (a) Probability:

Explanation / Answer

Since the PDF is uniformally distributed between the limits 0 and 1, so the probability of getting a mean greater than one is simply 1-0.57 = 0.43

No, it is not unusual to get a mean of 0.57 for a set of 100 randomly generated numbers because the PDF of the distribution shows that any value between 0 and 1 has equal probability of occurring. So a mean score of 0.57 is as likely to occur as 0.50

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