Question

Suppose the exam scores are normally distributed with a population mean of 78.2% and a standard deviation of 9.3%

a) What is the probability of a student getting a score of 90% or better?  (Round to four decimal places. This should be the theoretical probability that is calculated, NOT the empirical probability from the simulation.)

B)What is the probability of a class of 21 students having a mean of 90% or better?  (Round to six (6) decimal places.This should be the theoretical probability that is calculated, NOT the empirical probability from the simulation.)

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	78.2
std deviation   =σ=	9.3000

probability of a student getting a score of 90% or better:

probability =

P(X>90)

=

P(Z>1.269)=

1-P(Z<1.27)=

1-0.8977=

0.1023

b)

sample size       =n=	21
std error=σx̅=σ/√n=	2.0294

probability of a class of 21 students having a mean of 90% or better:

probability =

P(X>90)

=

P(Z>5.814)=

1-P(Z<5.81)=

1-1=

0.000000