Answer to Question #150596 in Statistics and Probability for Vladimyr Lubin

Question #150596
(6.4.7) Assume that females have pulse rates that are normally distributed with a mean of mu=76.0 beats per minute and a standard deviation of sigma=12.5 beats per minute.
a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute.
The probability is
1
Expert's answer
2020-12-17T08:31:41-0500

Let X=X= pulse rate: XN(μ,σ2)X\sim N(\mu, \sigma^2)

Then Z=XμσN(0,1)Z=\dfrac{X-\mu}{\sigma}\sim N(0, 1)

Given μ=76.0,σ=12.5\mu=76.0, \sigma=12.5


P(72<X<80)=P(X<80)P(X72)P(72<X<80)=P(X<80)-P(X\leq72)

=P(Z<807612.5)P(Z727612.5)=P(Z<\dfrac{80-76}{12.5})-P(Z\leq\dfrac{72-76}{12.5})

=P(Z<0.32)P(Z0.32)=P(Z<0.32)-P(Z\leq-0.32)\approx

0.6255160.374484=0.251032\approx0.625516-0.374484=0.251032

The probability is 0.251032.0.251032.


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