2. The information technology department at Stanford University recently conduct

Question

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?

Explanation / Answer

(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)

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