Question

For a normally distributed population with a mean of 35 and a standard deviation of 7.5, if a sample of 50 is taken from the population, what is the probability that the sample mean will be between 35 and 37.5?

Answer 1

mean =  = 35

standard deviation =  = 7.5

n = 30

 _{= 35}

 = ( /n) = (7.5 / 30 ) = 1.3693

P (35 <  < 37.5 )

P ( 35 - 35 / 1.3693) < (  -  /  ) < ( 37.5 - 35 / 1.3693 )

P ( 0 / 1.3693 < z < 2.5 / 1.3693 )

P ( 0 < z < 1.83 )

P ( z < 1.83 ) - P ( z < 0 )

Using z table

= 0.9664 - 0.5000

= 0.4664

Probability = 0.4664