Answer to Question #116010 in Statistics and Probability for Seifu

Question

The average grade/mark of all college students is 70 with standard deviation of 20. If a random sample of 49 students is taken, what is the probability that the sample average grade/mark is
a) At least 65
b) Less than 78
c) Between 65 and 72

Answer 1

sample mean μ_s=μ=70

sample standard deviation σ_s=σ/$\sqrt{n}=20/7=2.857$

a)P(x≥65)=1-P(x<65)

P(x<65), z=(x-μ_s)/σ_s=-1.75

using table P(x<65)=0.04

P(x≥65)=1-0.04=0.96=96%

b)P(x<78)

P(x<78), z=(78-70)/2.857=2.8

using table P(x<78)=0.9974=99.74%

c)P(65<x<72)=P(x<72)-P(x<65)

P(x<65)=0.04

P(x<72), z=(72-70)/2.857=0.7

using table P(x<72)=0.758

P(65<x<72)=0.758-0.04=0.718=71.8%