Question

Using the information below, answer the next two questions:

A study measures blood pressure among college students. The lowest actual blood pressure is 70, and the highest is 130. Each blood pressure test is equally likely. A sample of 100 students’ blood pressure is taken. The mean is 100 and the standard deviation is 17.321.

(a) What is the probability that the mean of blood pressure is less than 97. (Round to 4 decimal places)

(b)  Find the 90 percentile for the mean of 100 blood pressure. (Round to 2 decimal places)

Answer 1

Solution :

Given that ,

mean = $\mu$ = 100

standard deviation = $\sigma$ = 17.321

n = 100

$\mu$_{$\bar x$} = 100

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 17.321/ $\sqrt$ 100=1.73

P($\bar x$ < 97) = P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (97-100) / 1.73]

= P(z <-1.73 )

Using z table

= 0.0418

b.

Using standard normal table,

P(Z < z) = 90%

=(Z < z) = 0.90  

= P(Z < z ) = 0.90  

z = 1.28

$\bar x$ = z * $\sigma$ _{$\bar x$}+ $\mu$ _{$\bar x$}

$\bar x$ = 1.28*1.73+100

$\bar x$ = 102.21