Question

A population has a mean of 245.3 and a standard deviation of 12.6. A sample of 200 will be taken. Find the probability that the sample mean will be less than 248.4.

a) Calculate the z score. (Round your answer to 2 decimals.)

b) Find the probability that the sample mean will be less than 248.4. (Round your answer to 4 decimals.)

Answer 1

Solution :

Given that,

mean = = 245.3

standard deviation = = 12.6

n = 200

= 245.3

=  / n = 12.6/ 200=0.89

a

z =( - ) / = (248.4-245.3) / 0.89=3.48

b

P( < 248.4) = P[( - ) / < (248.4-245.3) / 0.89]

= P(z < 3.48)

Using z table  

= 0.9997   

probability= 0.9997