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Assume that females have pulse rates that are normally distributed with a mean of
mu equals μ=74.0 beats per minute and a standard deviation of
sigma equals 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 less than 80 beats per minute.
b. If 4 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 80 beats per minute.
c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

Respuesta :

MathPhys

Step-by-step explanation:

a. First, find the z-score.

z = (x − μ) / σ

z = (80 − 74.0) / 12.5

z = 0.48

Use a calculator or table to find the probability.

P(z < 0.48) = 0.6844

b. Find the standard deviation of the sample.

σₓ = σ / √n

σₓ = 12.5 / √4

σₓ = 6.25

Find the z-score.

z = (x − μ) / σ

z = (80 − 74.0) / 6.25

z = 0.96

Use a calculator or table to find the probability.

P(z < 0.96) = 0.8315

c. When the distribution of the population is normal, then the distribution of the sample mean is also normal.

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