Question: A dexterity test is administered by a private testing agency. The scores are normally distributed with a mean of 70 and standard deviation of 9.

A dexterity test is administered by a private testing agency. The scores are normally

distributed with a mean of 70 and standard deviation of 9.

a) A particular job requires candidates to score at least 80 on the test. What percentage

of candidates will be hired?

b) Find the 20th percentile.

c) What proportion of candidates have scores between 67 and 72?

d) Forty candidates arrive from U of T to take the test. What is the probability that the

average mark for this group of 40 students is between 67 and 72?

Please provide full solutions.

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