Question

For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as a systolic blood pressure above 140. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.

Answer 1

Hence, the required probability = 0.0001

Explanation:

Answer 2

Answer: 0.0001

Explanation:

Given : For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1.

i.e.
`\mu=114.8\ \ \ \&\ \ \sigma=13.1`

Sample size =4

Let x be the sample mean systolic blood pressure.

Then the probability that their mean systolic blood pressure is greater than 140 will be

`P(x>140)=1-P(x\leq140)\\\\=1-P((x-\mu)/((\sigma)/(√(n)))\leq(140-114.8)/((13.1)/(√(4))))\\\\\ =1-P(z\leq3.85)\ \ [\because \ z=(x-\mu)/((\sigma)/(√(n)))]\\\\=1-0.9999\ \ \text{[By z-table]}\\\\= 0.0001`

Hence, the required probability = 0.0001