Question

The ages of all college students follow a normal distribution with a mean of 27 years and standard deviation of 4.4 years. Find the probability that the mean age for a random sample of 36 students would be:

1. Between 25.5 and 28 years old
2. Less than 25.5 years old

Instructions:

Draw the normal curve and shade the area where applicable

Do not give calculator key strokes. (Give the formula used)

Circle your answer to the question.

Answer 1

This is a normal distribution question with

Sample size (n) = 36

Since we know that

a)

P(25.5 < x < 28.0)=?

This implies that

P(25.5 < x < 28.0) = P(-2.0455 < z < 1.3637) = P(Z < 1.3637) - P(Z < -2.0455)

P(25.5 < x < 28.0) = 0.9136689979678574 - 0.020402794603842655

b)

P(x < 25.5)=?

The z-score at x = 25.5 is,

z = -2.0455

This implies that

PS: you have to refer z score table to find the final probabilities.

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