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)
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
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