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. It follows a uniform distribution. [Sean Hint: The data distribution has mean 100 and standard deviation 17.32]. A sample of 100 students’ blood pressure is taken.

(a) What is the probability that the mean of blood pressure is less than 97. [Hint:First use the mean and std. deviation given in hint to compute the distribution of sampling distribution of the sample mean .].   (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 = = 100

standard deviation = = 17.32

n = 100

=   = 100

= / n = 17.32/ 100 = 1.732

a) P( < 97) = P(( - ) / < (97 - 100) / 1.732)

= P(z < -1.73)

Using z table

= 0.0418

  b) Using standard normal table,

P(Z < z) = 90%

= P(Z < z) = 0.90

= P(Z < 1.282) = 0.90

z = 1.282

Using z-score formula  

= z * +

= 1.282 * 1.732 + 100

= 102.22