Question

In an examination the probability distribution of scores (X) can be approximated by normal distribution with...

In an examination the probability distribution of scores (X) can be approximated by normal distribution with mean 63.2 and standard deviation 7.6.

*Please explain how you got your answers.

1) Suppose one has to obtain at least 55 to pass the exam. What is the probability that a randomly selected student passed the exam? [Answer to 3 decimal places]

Tries 0/5

2) If two students are selected randomly what is the chance that both the students failed? [Answer to 3 decimal places]

Tries 0/5

3) If only top 8% students are given an award, then what was the minimum marks required to get the award? [Answer to 1 decimal place]

Homework Answers

Answer #1

a)
mean= 63.20
sd= 7.60

P( X>55)
= 1 - P(X<55)

I know that, z = (X-mean)/(sd)
z1 = (55-63.2)/7.6)
z1= -1.0789

hence,
P( X>55)
=1- P(Z<-1.0789)
1 - NORMSDIST(-1.0789)
0.860

b)
mean= 63.2
sd= 7.6
n= 2

P(X < 55)
I know that, z = (X-mean)/(sd/sqrt(n))
z1 = (55-63.2)/7.6/sqrt(2))
z1= -1.5259

hence,
P(X < 55)=
= P(Z<-1.5259)
NORMSDIST(-1.5259)
0.064

c)
P(Z<z) 92%
z= NORMSINV(0.92)
z= 1.40507156
I know that, z = (X-mean)/sd
(X-mean)/sd = 1.4051
X= 1.4051*7.6+63.2
X= 73.9

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