Assume that the marks of students in Statistical Methods are normally distributed.

Assume that the marks of students in Statistical Methods are normally distributed. A random sample of 25 students’ marks yields a sample mean of 70 and a sample standard deviation of 10.
(a) Estimate the population mean of the marks with 95% confidence.
(b) If the population mean of the marks is 67 and the probability that the sample mean of 25 students’ marks is greater than 70 is 3%. Find the population standard deviation of the marks.

(c) A child psychologist was interested in the difference in age (in years) between a boy and a girl when they first learn to ride a two-wheeled bicycle. The psychologist calculated a 99% confidence interval for the difference in age to be (-0.58, 0.71). Can he conclude that there is no difference in age, on the average, at which boys and girls learn to ride a two-wheeled bicycle?