What is the probability that five randomly selected students will have a mean score that is greater than the mean achieved by the students in the previous problem? (Round your answer to 4 decimal places.

the probability that five randomly selected students will have a mean score that is greater than the mean achieved by the students = 0.0096

Step-by-step explanation:

From the five randomly selected students; 160, 175, 163, 149, 153

mean average of the students = 160+175+163+149+153/5

= mean = x-bar = 800/5

mean x-bar = 160

from probability distribution, P (x-bar > 160) = P[ x-bar - miu / SD > 160 - 150.8 / 3.94]

P (Z>2.34) = from normal Z-distribution table

= 0.0096419

= 0.0096

hence the probability that five randomly selected students will have a mean score that is greater than the mean achieved by the students = 0.0096

where SD = standard deviation = 3.94 and Miu = 150.8