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.

Answer 2

From the information given, the 10th percentile will be 63.

How to calculate the percentile.

From the information given, it was stated that the mean is 73 and the standard deviation is 8.

Then, we will look that the normal z table, this will be:

= P (z < -1.282) = 0.10

Therefore, (x - 73)/8 = -1.282

x = (-1.282)(8) + 73

x = 62.74

x = 73

The 10th percentile is 73.

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