Answer:
Option A - 0.9938
Step-by-step explanation:
Given : Assume that blood pressure readings are normally distributed with a mean of 118 and a standard deviation of 6.4. If 64 people are randomly selected.
To find : The probability that their mean blood pressure will be less than 120?
Solution :
The formula to find the probability is
[tex]P(Z=X)=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Where, X is the sample mean
[tex]\mu=118[/tex] is the population mean
[tex]\sigma=6.4[/tex] is the standard deviation
n=64 is the number of sample
The probability that their mean blood pressure will be less than 120 is given by,
[tex]P(Z<120)=\frac{120-118}{\frac{6.4}{\sqrt{64}}}[/tex]
[tex]P(Z<120)=\frac{2}{\frac{6.4}{8}}[/tex]
[tex]P(Z<120)=\frac{2}{0.8}[/tex]
[tex]P(Z<120)=2.5[/tex]
From the z-table the value of z at 2.5 is
[tex]P(Z<120)=0.9938[/tex]
Therefore, Option A is correct.
The probability that their mean blood pressure will be less than 120 is 0.9938.
