Jim\'s systolic blood pressure is a random variable with a mean of 147 mmHg and

Question

Jim's systolic blood pressure is a random variable with a mean of 147 mmHg and a standard deviation of 17 mmHg. For Jim's age group, 140 is the threshold for high blood pressure. Assume the data given follows the normal probability distribution. (a) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 144 or less? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be 174 or more? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.) If Jim's systolic blood pressure is taken at a randomly chosen moment, what is the probability that it will be between 126 and 172? (Round the value of z to 2 decimals. Use Appendix C-2 to find probabilities. Round your final answer to 4 decimals.)

Explanation / Answer

mean is 147 and standard deviation is 17

a) P(x<144)=P(z<(144-147)/17)=P(z<-0.18) or 1-P(z<0.18). from normal distribution table we get 1-0.5714=0.4286

b) P(x>174)=P(z>(174-147)/17)=P(z>1.59) or 1-P(z<1.59), from normal distribution table we get 0.05592

c) P(126<x<172)=P((126-147)/17<z<(172-147)/17)=P(-1.24<z<1.47) or P(z<1.47)-(1-P(z<1.24))=0.9292-(1-0.8925)=0.8217

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