Question

What is the 10th percentile, n of group of people's pulse rates, where X = pulse rates of group of people, for which the mean is 73 and the standard deviation is 8? Assume a normal distribution. (Round your answer to the nearest whole number.)

Answer 1

Answer:

The 10th percentile is 63 pulse rate.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  73

Standard Deviation, σ = 8

We are given that the distribution of pulse rates of group of people is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.10

$P( X < x) = P( z < \displaystyle\frac{x - 73}{8})=0.10$ Calculation the value from standard normal z table, we have,  

$P(z < -1.282) = 0.10$

$\Rightarrow \displaystyle\frac{x - 73}{8} = -1.282\\\\x = (-1.282)(8) + 73 \\\\x = 62.744 \approx 63$

Thus, the 10th percentile is 63 pulse rate.