Question

Assume that females have pulse rates that are normally distributed with a mean of mu equals 75.0 μ=75.0 beats per minute and a standard deviation of sigma equals 12.5 σ=12.5 beats per minute. Complete parts​ (a) through​ (c) below. a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 71 71 beats per minute and 79 79 beats per minute. The probability is . 2510 .2510 . ​(Round to four decimal places as​ needed.) b. If 16 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean between 71 71 beats per minute and 79 79 beats per minute. The probability is nothing . ​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

mean = = 75.0

standard deviation = = 12.5

a.

P(71 < x < 79) = P[(71 - 75.0)/ 12.5) < (x - ) /  < (79 - 75.0) / 12.5) ]

= P(-0.32 < z < 0.32)

= P(z < 0.32) - P(z < -0.32)

= 0.6255 - 0.3745

= 0.2510

Probability = 0.2510

b.

= / n = 12.5 / 16 = 3.125

= P[(71 - 75.0) / 3.125< ( - ) / < (79 - 75.0) / 3.125)]

= P(-1.28 < Z < 1.28)

= P(Z < 1.28) - P(Z < -1.28)

= 0.8997 - 0.1003  

= 0.7994

Probability = 0.7994