1 answer

In a recent study, the Centers for Disease Control reported that diastolic blood pressures of adult...

Question:

In a recent study, the Centers for Disease Control reported that diastolic blood pressures of adult women in the U.S. are app
In a recent study, the Centers for Disease Control reported that diastolic blood pressures of adult women in the U.S. are approximately normally distributed with a mean of 80.5 and standard deviation 9.9. Round all answers to 4 decimal places. a. What proportion of women have blood pressures lower than 70? b. Find the 30th percentile for blood pressures. C. Suppose a sample of 150 women is taken. What is the probability that the sample mean blood pressure would be between 75 and 80?

Answers

Here

mean=\mu =80.5

Standard deviation = \sigma = 9.9

a)

P(X<70)=P(\frac{X-\mu }{\sigma }<\frac{70-80.5}{9.9})

= P(Z < -1.06

= 0.1446 ( from standard normal table )

Therefore, the proportion of women that have blood pressures lower than 70 is 0.1446

b)

P(X<x)=0.30

P(\frac{X-\mu }{\sigma }<\frac{x-80.5}{9.9})=0.30

  P(Z<z)=0.30

From Standard normal table, the z-critical value corresponding to the closest probability of 0.30 is -0.52

i.e. z = -0.52

Now

X=\mu +z\sigma =80.5+(-0.52)*9.9= 75.352

The 30th percentile for blood pressure is 75.352

c)

Here

n = 150

P(75<\overline{x}<80)=P(\frac{75-80.5}{9.9/\sqrt{150}}<\frac{\overline{x}-\mu }{\sigma /\sqrt{n}}<\frac{80-80.5}{9.9/\sqrt{150}})

  =P(-6.80<Z<-0.62)

  =P(Z<-0.62)-P(Z<-6.80)

=0.2676 -0.0000

  =0.2676

The probability that the sample mean blood pressure would be between 75 and 80 is 0.2676

.

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