Question

2. The distribution of heights for the population of females in Canada is approximately normally distributed with a mean of 67.3 inches and a standard deviation of 7 inches.
   1. What is the probability that a randomly selected female is shorter than 65 inches?
3. 2. What is the probability that she is between 65 and 70 inches tall?
   3. Above what height does one find the tallest 10% of the population?
   4. What is the probability that among three females selected at random from the population, at least one will have a height outside the range of 65 to 70 inches?

** For this question, carry four decimal places.

Answer 1

Let X be a random variable representing the height of a female in Canada. Then X is normally distributed with mean = and standard deviation

(a)  The probability that a randomly selected female is shorter than 65 inches=

To get the probability value 0.371 you can use standard normal distribution calculator or standard normal table.

(a)  the probability that she is between 65 and 70 inches tall=

(b)

Let above height h inches one finds the tallest 10% of the population.

Then

we know that

Then so, h=76.274 inches

(c) Let p=Probability that one will have a height outside the range of 65 to 70 inches

Then using previous answer

Now we shall use Binomial distribution with n=3, p=0.721

Let Y= number of females having a height outside the range of 65 to 70 inches

Then Y is Binomial random variable with probability of success p=0.721