Large Sample Tests

#1
I need help with this question. Can anyone help explain how the answers below were obtained. Thanks in advance.



The frequency distribution of the heights (measured in feet) of the entire Martian army is as follows:

Height Relative Frequency
4 2/5
5 1/5
6 1/5
7 1/5

a) A squad of 64 Martians is selected at random from the Martian army to train for special undercover operations. What is the probability that the mean height of this squad will be greater than 5.5 feet?

b) A second squad of 36 Martians is also selected from the Martian army. These 36 are all experts at extrasensory perception (ESP) and, on Mars, it is believed that ESP experts are taller then the average Martian soldier. Is there any truth to this belief, if the sample of 36 has a mean height of 5.75 feet and α less than or equal to .01?



a) 0.0197
b) Z = 2.83, reject Ho, the ESP soldiers are significantly taller