A health study reported that in one country systolic blood p

A health study reported that, in one country, systolic blood pressure readings have a mean of 116 mm Hg and a standard deviation of 16 mm Hg. A random sample of 25 adults from this country is taken. Assume systolic blood pressure readings are normally distributed. Find the probability that the sample mean reading is within 10 mm Hg of the mean for the country.

.4680

.9982

0.00

.95

Solution

Given

A health study reported that, in one country, systolic blood pressure readings have a mean of 116 mm Hg and a standard deviation of 16 mm Hg. A random sample of 25 adults from this country is taken. Assume systolic blood pressure readings are normally distributed.

we ahve to find the probability that the sample mean reading is within 10 mm Hg of the mean for the country.

let X denote systollic blood pressure

then X follows normal distribution with mean =116 standerd deviation =16

then

sample mean also foolows normal distribution with mean=116 standerd deviation 16/5 =3.2

so we have to find

P(116 -10 <sample mean < 116+10)=?

now

P(116-10 <sample mean<116+10)=P(-10 <sample mean -116 < 10)

                                                 =P({-10/3.2} <[{sample mean -116}/3.2] <{10/3.2})

                                                =P(-3.125 < Z < 3.125)

                                                =P(Z<3.12) - P(-3.12)

                                                =0.99910 -0.00090     ( from standerd normal distribution table)

                                                 =   0.9982 answer

where

Z =[{sample mean - 116}/3.2]

Z follows standerd normal distribution