Normal and Sampling Distributions question

Q1.

The life of cell batteries is normally distributed with a mean of 88.2 hours and a standard deviation of15.5 hours. 93% of the batteries will last more than how many hours? (2 decimal places )

Q2.

Simulated data is frequently used in economic research. An example of how asimulated data set may be constructed is through using arandom number generator. Consider when random numbers between 0 and 1 are generated, with each generated number having four decimal places. Now decide that a sample of 10,000 randomly generated numbers is to be selected. These 10,000 numbers will form what is called a data set.

If the mean of distribution of the individual random numbers between 0 and 1 is 0.5 and the variance 1/12, calculate:

a) The probability that a randomsample of 10,000 numbers (a data set) will have a sample mean of at least 0.499 (Answer to 4 decimal places):

b) Using the probability from part a, if 5,000 data sets include 10,000 random numbers, how many of these data sets would be expected to have a sample mean of at least 0.499 (calculate to the nearest whole number)? Answer:

Q3.

The length of time for long-distance phone calls has been found to be normally distributed, with a mean of 23.2 minutes and a standard deviation of6.7 minutes. In a randomly selected sample of59 calls, what is the sample average call time below which 10% of sample average call times will be shorter? (2 decimal places)