Question

The scores of individual students on the American College Testing (ACT) program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. Forty-nine randomly selected seniors take the ACT test. What is the probability that their mean score is less than 18? Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 18.6

standard deviation = = 6

n = 49

= 18.6

=  / n = 6 / 49=0.857

P( < 18) = P[( - ) / < (18-18.6) /0.857 ]

= P(z < -0.70)

Using z table  

= 0.2420