Question

if exam 1 grades are normally disributed witj mean of 70 & sd 10 find probability a random selected student recives a 60 (b)less than 60 (c)between 65&85 d more than 70

Answer 1

Solutions:

Given that,
μ =70 , σ=10
A)P(X=60)= )= p{[(x- μ)/σ]=[(60- 70)/10]}
=P(z=-1)
=0.1587 ( from Standard Normanl table)
B) P(X< 60)= p{[(x- μ)/σ]<[(60 - 70)/10]}
=P(z<-1)
=0.1587 ( from Standard Normanl table)
C)

P(65<X<85 )= p{[(65 - 70)/10]<[(x- μ)/σ]<[(85 - 70)/10]}
=P(-0.5<Z<1.5)
= p(Z<1.5) - p(Z< -0.5)
= 0.9332 - 0.3085 ( from. Standard Normanl table)
=0.6247
D)P(X>70)=1-P(X<=70)
=1- p{[(x- μ)/σ]<=[(70 - 70)/10]}
= 1- P(z<= 0)
=1-0.5 ( from Standard Normanl table)
=0.5