. Use the formula for z and the z distribution (normal table) to solve the following problems. Be sure to
include a diagram for each question and carry to 2 decimal places. The time it takes an elementary
student to complete a standardized fitness test may be looked upon as a random variable having a
normal distribution with a mean µ = 38.8 minutes and standard deviation σ = 12.6 minutes. Find the
probabilities that a student will complete the fitness test in a) At least 40 minutes? (1.5 points) b)
Between 10 and 30 minutes? c) At most 60 minutes? d) Between 30 and 50 minutes?
3. A marketing group is trying to improve sales for a clothing retail store, but first they are trying to
determine the age demographics of customers based on store membership profiles that state the date
of birth on it. The age of customers/members is normally distributed with a mean of 26.7 years and a
standard deviation of 3.9 years. How old should the marketing group expect the 75 th percentile of the
store customers to be based on their membership date of birth? You will have to use the formula for z
and the z distribution (normal table) to solve this problem. Be sure to include a diagram.
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