Question

2) Suppose that a random variable X is skewed with µ = 100 and σ =16. Is it possible to find the probability that X is less than 96?

Select one:

A) Yes, it is possible, P(X < 96) = P(Z < -0.25) = 0.5987.

B) We cannot find this probability because, apart from being described as "skewed", we are not provided with any further information about the probability distribution of X.

C) Yes, it is possible.

D) Yes, it is possible, P(X < 96) = P(Z < -0.25) = 0.4013.

3) Heights of males are normally distributed with a mean of 165 cm and a standard deviation of 10 cm. What is the probability that the sample mean height of males is less than 170 cm for a random sample of 25 males?

Select one:

A) None of these choices is correct.

B) P(x¯<170)=P(Z<170−16510/25√=P(Z<0.5)=0.6915P(x¯<170)=P(Z<170−16510/25=P(Z<0.5)=0.6915

C) P(x¯<170)=P(Z<170−16510/25√=P(Z<2.5)=0.9938P(x¯<170)=P(Z<170−16510/25=P(Z<2.5)=0.9938

D) P(x¯<170)=P(Z<170−16510/25√=P(Z<2.5)=0.0062

Answer 1

2)

X ~ N ( µ = 100 , σ = 16 )
P ( X < 96 ) = ?
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 96 - 100 ) / 16
Z = -0.25
P ( ( X - µ ) / σ ) < ( 96 - 100 ) / 16 )
P ( X < 96 ) = P ( Z < -0.25 )
P ( X < 96 ) = 0.4013

3)

X ~ N ( µ = 165 , σ = 10 )
P ( X̅ < 170 ) = ?  
Standardizing the value
Z = ( X - µ ) / (σ/√(n)
Z = ( 170 - 165 ) / ( 10 / √25 )
Z = 2.5
P ( ( X - µ ) / ( σ/√(n)) < ( 170 - 165 ) / ( 10 / √(25) )
= P ( Z < 2.5 )
P ( X̅ < 170 ) = 0.9938