Answer:
99.38%
Step-by-step explanation:
We have that the mean (m) is equal to 124, the standard deviation (sd) 6.4 and the sample size (n) = 64
They ask us for P (x <126)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (126 - 124) / (6.4 / (64 ^ 1/2))
z = 2.5
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <2.5) = 0.9938
The probability is 99.38%
According to the normal distribution table, the probability that their mean blood pressure will be less than 126 is 99.38%.
Given :
Blood pressure readings are normally distributed with a mean of 124 and a standard deviation of 6.4.
The formula of z-score is used to determine the probability that their mean blood pressure will be less than 126. The formula of z score is given by:
[tex]\rm z = \dfrac{x-m}{\dfrac{\sigma }{\sqrt{n} }}[/tex]
Now, substitute the values of known terms in the above equation.
[tex]\rm z = \dfrac{126-124}{\dfrac{6.4 }{\sqrt{64} }}[/tex]
[tex]\rm z = \dfrac{2}{\dfrac{6.4 }{8}}[/tex]
Further, simplify the above expression.
z = 2.5
According to the normal distribution table, the probability that their mean blood pressure will be less than 126 is:
P(z < 2.5) = 0.9938
So, the probability is 99.38%.
For more information, refer to the link given below:
https://brainly.com/question/21586810
