Question

For a normally distributed population with μ = 80 and σ = 20, if you sample randomly...

a. what is the probability of obtaining a score (n=1) between 78 and 82?

b. what is the probability of obtaining a mean between 78 and 82 if n=4?

c. what is the probability of obtaining a mean between 78 and 82 if n=25?

Answer 1

Part a ) P ( 78 < X < 82 )

Standardizing the value

P ( 78 < X < 82 ) = ( - 0.10 < Z < 0.10 )

P ( 78 < X < 82 ) = P ( Z < 0.10 ) - P ( Z < - 0.10 )

P ( 78 < X < 82 ) = 0.5398 - 0.4602

P ( 78 < X < 82 ) = 0.0797

Part b)   P ( 78 < X < 82 )

P ( 78 < X < 82 ) = ( - 0.20 < Z < 0.20 )

P ( 78 < X < 82 ) = P ( Z < 0.20 ) - P ( Z < - 0.20 )

P ( 78 < X < 82 ) = 0.5793 - 0.4207

P ( 78 < X < 82 ) = 0.1585

Part c)  P ( 78 < X < 82 )

P ( 78 < X < 82 ) = ( - 0.50 < Z < 0.50 )

P ( 78 < X < 82 ) = P ( Z < 0.50 ) - P ( Z < - 0.50 )

P ( 78 < X < 82 ) = 0.6915 - 0.3085

P ( 78 < X < 82 ) = 0.3829