A health study reported that in one country, systolic blood preassure reading ha

Question

A health study reported that in one country, systolic blood preassure reading hav a mean of 117 and a standard deviation of 19. A reading above 140 is considered to be high blood pressure. Complete parts a through d below.

a. What is the z-score for a blood pressure reading of 140?

b. The proportion with high blood pressure is ?

c. What proportion of the populatin has systolic blood pressure in the range from 98 to 140?

d. Find the 90th percentile blood pressure readings.

Please post the work because I don't understand this question.

Explanation / Answer

Mean is 117 and s is 19

a) z score is (x-mean)/s =(140-117)/19=1.21

b) P(x>140)=P(z>(140-117)/19)=P(z>1.21) or 1-P(z<1.21) , from normal distribution table we get 1-0.8869=0.1131

c) P(98<x<140)=P((98-117)/19<z<(140-117)/19)=P(-1<x<1.21) or P(z<1.21)-(1-P(z<1))=0.8869-(1-0.8413)=0.7282

d) for 90% the z value is 1.28

thus answer is mean+z*s=117+1.28*19=141.32

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