Question

According to a research​ institution, men spent an average of ​$132.63 on​ Valentine's Day gifts in 2009. Assume the standard deviation for this population is ​$40 and that it is normally distributed. A random sample of 10 men who celebrate​ Valentine's Day was selected. Complete parts a through e.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than ​$125​?

c.What is the probability that the sample mean will be more than ​$140​?

d.What is the probability that the sample mean will be between ​$115 and ​$155​?

e. Identify the symmetrical interval that includes​ 95% of the sample means if the true population mean is ​$132.63

Answer 1

µ = 132.63

sd = 40

n = 10

a) standard erro = sd / sqrt(n) = 40 / sqrt(10) = 12.65

b)

                               

                                = P(Z < -0.6)

                                = 0.2743

c)

                               

                                = P(Z > 0.58)

                                = 1 - P(Z < 0.58)

                                = 1 - 0.7190

                                = 0.2810

d)

                                             

                                              = P(-1.39 < Z < 1.77)

                                              = P(Z < 1.77) - P(Z < -1.39)

                                              = 0.9616 - 0.0823

                                              = 0.8793

e) Z for 95% interval = Z_0.025 = 1.96

Symmetrical interval

                                

                                 = (107.838 , 157.422)