Answer to Question #167567 in Statistics and Probability for kmy

Question

1. Information from the Department of Motor Vehicles indicates that the average age of  licensed drivers is 38.6 years with a standard deviation of 10.4 years. Assume that the  distribution of the driver’s ages is normal.  

a. What proportion of licensed drivers are from 25 to 45 years old?

b. Determine the ages of licensed drivers separating the upper 10% and lower 10%  percent of the population.

2. Weights of newborn babies in a particular city are normally distributed with a mean of  3380 g and a standard deviation of 475 g. 

a. A newborn weighing less than 2100 g is considered to be at risk, because the  mortality rate for this group is very low. If a hospital in the city has 500 births in a  year, how many of those babies are in the “at-risk” category?

b. If we redefine a baby to be at risk if his or her birth weight is in the lowest 3%,  find the weight that becomes the cutoff separating at-risk babies from those who  are not at risk.

c. If 20 newborn babies are randomly selected as a sample in a study, find the  probability that their mean weight is between 3200 g and 3500 g.

3. Over the past 30 games between team A and team B, team A has won 14 times, team B has won 11 times and the game has ended in a draw 5 times. If these two teams played 9  games this season, what is the probability that team �� would win 5 games, team �� would  win 3 games, and the remaining game would be a draw?

4. The formula for the standard error (standard deviation of the distribution of sample  means) implies that as the sample size (n) increases, the size of the standard error  decreases. Explain the role of the standard error in comparing the sample mean and the  population mean. Use the definitions and concepts on sample means distribution and  standard error and show examples comparing the sample mean and the population mean  of a distribution when the standard error changes in value to express your answer.

Answer 1

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