Question

The ages of a group of 50 women are approximately normally distributed with a mean of 48 years and a standard deviation of 5 years. One woman is randomly selected from the​ group, and her age is observed. a. Find the probability that her age will fall between 56 and 60 years. b. Find the probability that her age will fall between 47 and 51 years. c. Find the probability that her age will be less than 35 years. d. Find the probability that her age will exceed 40 years.

ANSWER THE FF: a. The probability that her age will fall between 56 and 60 years is ​(Round to three decimal places as​ needed.) b.The probability that her age will fall between 47 and 51 yrs is ​(Round to three decimal places as​ needed.) c. ​Find the probability that her age will be less than 35 years.(Round to three decimal places as​ needed.) d. Find the probability that her age will exceed 40 years. ​(Round to three decimal places as​ needed.)

Answer 1

Let X be the age of a randomly selected woman. Now, X follows a Normal (48, 5) distribution

a) P(56<X<60) = P(56-48/5<Z<60-48/5) = P(1.6<Z<2.4) = P(Z<2.4) - P(Z<1.6) = 0.99180-0.94520 = 0.0466 ie 0.047(rounded)

b) P(47<X<51) = P(-0.2<Z<0.6) = P(Z<0.6) - P(Z<-0.2) = 0.72575- (1-0.57926) = 0.305 (rounded answer)

c) P(X<35) = P(Z<-2.6) = 1 - P(Z<2.6) = 1- 0.99534 = 0.005 (rounded)

d) P(X>40) = P(Z>-1.6) = P(Z<1.6) = 0.992