The height, in meters, of adult male African elephants may be assumed to be normally distributed with mean and standard deviation of 0.20. The heights of a sample of 12 such elephants were measured with the following results, in meters.

3.37 3.45 2.93 3.42 3.49 3.67 2.96 3.57 3.36 2.89 3.22 2.91

The mean of the above 12 numbers is 3.27

(a) State the point estimate of the mean height of adult male African elephants.

(b) Calculate the margin of error for a 90% confidence interval estimate for the mean height

(c) Construct a 90% confidence interval: (,)

(d)What sample size is needed so that the error is no more than 0.01 m? n =elephants.

(WHEN NECESSARY, ROUND ALL FINAL ANSWERS TO 2 DECIMAL PLACES)