Question

Suppose systolic blood pressure of 17-year-old females is approximately normally distributed with a mean of 113 mmHg and a standard deviation of 24.71 mmHg. If a random sample of 22 girls were selected from the population, find the following probabilities:

a) The mean systolic blood pressure will be below 109 mmHg. probability =

b) The mean systolic blood pressure will be above 118 mmHg. probability =

c) The mean systolic blood pressure will be between 106 and 125 mmHg. probability =

d) The mean systolic blood pressure will be between 106 and 113 mmHg. probability =

Answer 1

The information of systolic blood pressure of 17 year old females is given and it is approximately normally distributed with mean and a standard deviation of . Now a random sample of girls is selected from the population and we need to find the following probabilities asked in the question.

To fin the probabilities we first have to find the standardized scores for the given systolic blood pressure, and the formula for calculating the standardized score is-

where sample mean

(a) Given:

Now the probability that the mean systolic blood pressure will be below 109mmHg is -

Hence, the probability that the mean systolic blood pressure will be below 109mmHg is 0.22385 Or 22.385%

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(b) Given:

Now,

                      

                       

                       

Hence, the probability that the mean systolic blood pressure will be above 118mmHg is 0.17129 Or 17.129%

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(c) Now we have to find the probability that the mean systolic blood pressure will be between 106 and 125 mmHg, so to find this we have to find the standardized scores for 106 and 125 mmHg and the we will find the probability.

When

When

Now,

                                   

                                    

                                    

Hence, the probability that the mean systolic blood pressure will be between 106 and 125 mmHg is 0.89666 Or 89.666%

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(d) Now we have find the probability that mean systolic blood pressure will be between 106 and 113 mmHg.

When

When

Now,

                                   

                                   

                                   

Hence, the probability that the mean systolic blood pressure will be between 106 and 113 mmHg is 0.40803 Or 40.803%