Question 1 Please be careful with the rounding and try to use all decimal places when possible

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of260feet and a standard deviation of56feet. We randomly sample 49 fly balls.

Part (a)

IfX= average distance in feet for 49 fly balls, then give the distribution ofX.

Round your standard deviation to two decimal places.

X~_____(_________,_________)

Part (b)

What is the probability that the 49 balls traveled an average of less than248feet? (Round your answer to four decimal places.)

____________

Part (c)

Find the60thpercentile of the distribution of the average of 49 fly balls. (Round your answer to two decimal places.)

__________ft

Question 2 Please be careful with the rounding and try to use all decimal places when possible

Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of males from a certain country. Forty-seven males are surveyed from a particular country. The sample mean is72inches.The sample standard deviation is2.6inches.

Part a

Find the following. (Enter exact numbers as integers, fractions, or decimals.)

(i)x=

(ii)=

(iii)n=

Part b

Construct a 95% confidence interval for the population mean height of males of this country.

(i) State the confidence interval. (Round your answers to two decimal places.)

(____________,_____________)

(ii) Sketch the graph.

(iii) Calculate the error bound. (Round your answer to two decimal places.)

Thank you for your help it much appreciated