Question

The score for a special personality test are normally distributed with a mean of 60 and standard deviation of 6. a) What is the probability that one person who took the test, chosen at random, will have scored less than 65? b) Random samples of 16 people who took the test are surveyed. What is the probability that the mean of these samples is less than 65?

Answer 1

Solution :

Given that,

mean = = 60

standard deviation = =6

(A)n = 1

= 60

=  / n = 6 / 1=6

P( <65 ) = P[( - ) / < (65-60) /6 ]

= P(z <0.83 )

Using z table  

= 0.7967   

probability= 0.7967

(B)

n = 16

= 60

=  / n = 6 / 16=1.5

P( <65 ) = P[( - ) / < (65-60) /1.5 ]

= P(z <3.33)

Using z table  

= 0.9996   

probability= 0.9996