Question

A -In one of Arizona’s lotteries, balls are numbered 1 through 35. Five balls are randomly selected

without replacement. The order of the selection does not matter. To win, your numbers must match

the ones selected. Find the probability of winning this lottery. Either round the probability to 3 significant

digits or express your answer as a fraction.

B. The distribution for ages of licensed drivers has a mean of 44.5 years and a standard deviation of

17.1 years. Assuming the distribution of ages is normally distributed, what percentage of drivers are

older than 25 years of age? Round your answer to 3 significant digits.

C. In a group of 14 persons, 6 are Republicans and 8 are Democrats. If five persons are randomly

selected from this group without replacement, find the probability that exactly 3 are Republicans?

Round answer to 3 significant digits.

D. The height standard for service in the U.S. Air Force is 64 inches to 77 inches. Females have

heights that are normally distributed with a mean of 63.8 inches and a standard deviation of 2.5”. If

225 random women are chosen from the population, how many of them would meet the height

qualifications to be in the Air Force? Round your answer to the nearest whole number.

Answer 1

A)

The probability of winning this lottery = 5C5/35C5

= 1/35C5 =

B)

Mean = 44.5 years

Standard deviation = 17.1 years

The required probability = P(X > 25)

= P{Z > (25 - 44.5)/17.1}

= P(Z > -1.14)

= 87.29%

C)

The required probability = 6C3 * 8C2/14C5

= 0.280

D)

Mean = 63.8 inches

Standard deviation = 2.5 inches

The required probability = P(64 < X < 77)

= P{(64 - 63.8)/2.5 < Z < (77 - 63.8)/2.5}

= P(0.08 < Z < 5.28)

= 0.4681

Number of women Expected to meet the height qualifications = 0.4681*225 ≈ 105