Answer to Question #150125 in Statistics and Probability for Colton elrod

Question

Assume that females have pulse rates are normally distributed with a mean of 76 bpm and a standard deviation of 12.5 bpm is 16 females randomly selected find the probability of pulse rates for the main less than 83 bpm

Answer 1

n = 16

Mean μ = 76

Standard deviation σ = 12.5

$μ\bar{X} = μ = 76 \\ σ\bar{X} = \frac{σ}{\sqrt{n}} = \frac{12.5}{\sqrt{16}} = 3.125 \\ P(\bar{X} < 83) = P(\frac{\bar{X} – μ\bar{X}}{σ\bar{X}} < \frac{83 – 76}{3.125}) \\ P(z < 2.24) = 0.9874$

Answer: 98.74 %