2 The information technology department at Stanford Universi

2. The information technology department at Stanford University recently conducted a study to find the average amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The research showed that the student population studied an average of 20 hours per week with a standard deviation of 10 hours.

(a) What is the standard error of the mean?

(b) What is the probability that a sample mean would exceed 20 hours per week?

(c) What is the probability of finding a sample mean less than 18 hours?

(d) What is the probability that average student study time is between 18 and 22 hours?

Solution

(a) What is the standard error of the mean?

standard error = s/vn

=10/sqrt(144)

=0.8333333

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(b) What is the probability that a sample mean would exceed 20 hours per week?

P(xbar>20) = P((xbar-mean)/(s/vn) >(20-20)/0.8333333)

=P(Z>0) =0.5 (from standard normal table)

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(c) What is the probability of finding a sample mean less than 18 hours?

P(xbar<18) = P(Z<(18-20)/0.8333333)

=P(Z<-2.4) = 0.0082 (from standard normal table)

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(d) What is the probability that average student study time is between 18 and 22 hours?

P(18<xbar<22) = P(-2.4<Z<(22-20)/0.8333333)

=P(-2.4<Z<2.4) = 0.9836(from standard normal table)