Question

Assume that females have pulse rates that are normally distributed with a mean of μ=75.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts​ B

B. If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 82 beats per minute.

Answer 1

Data given:
Mean = 75, SD/root(N) = 3.125, P(68 < Y < 82) = ?;

P(68 < Y < 82) = P(68 - mean < Y - mean < 82 - mean)
                  = P((68 - mean)/(SD/root(N)) < (Y - mean)/(SD/root(N)) < (82 - mean)/(SD/root(N)))
                  = P((68 - mean)/(SD/root(N)) < Z < (82 - mean)/(SD/root(N)))
                  = P((68 - 75)/3.125< Z < (82 - 75)/3.125)
                  = P(-2.24 < Z < 2.24)
                  = P(Z < 2.24) - P(Z <-2.24)
                  = 0.9752