Question

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

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 82 beats per minute.

b. If 16 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 82 beats per minute.

Answer 1

Solution :

Given that ,

mean = = 75.0

standard deviation = = 12.5

a) n = 1

= 75.0 and

= / n = 12.5 / 1 = 12.5

P( < 82) = P(( - ) / < (82 - 75.0) / 12.5)

= P(z < 0.56)

Using standard normal table,

= 0.7123

Probability = 0.7123

b)n = 16

= 75.0 and

= / n = 12.5 / 16 = 3.125

P( < 82) = P(( - ) / < (82 - 75.0) / 3.125)

= P(z < 2.24)

Using standard normal table,

= 0.9875

Probability = 0.9875