Question

# The scores of individual students on the American College Testing (ACT) program composite college entrance examination...

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.

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

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