Question

Blood pressure: High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.3. A sample of 32 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. ol. Part 1 of 5 Is it appropriate to use the normal approximation to find the probability that more than 44% of the people in the sample have high blood pressure? It is not appropriate to use the normal curve, since np - 9.6 10 and n (1 - p) - 22.4 10. Part 2 of 5 A new sample of 78 adults is drawn. Find the probability that more than 42% of the people in this sample have high blood pressure. The probability that more than 42% of the people in this sample have high blood pressure is 0.0104 Part: 2/5 Part 3 of 5 Find the probability that the proportion of individuals in the sample of 78 who have high blood pressure is between 0.22 and 0.32. The probability that the proportion of individuals in the sample of 78 who have high blood pressure is between 0.22 and 0.32 is 0.7127

Answer 1

Answer:

a)

Given,

It is not appropriate to use the normal curve since np = 32*0.3 = 9.6 < 10 & nq = 32*0.7 = 22.4 >= 10

b)

P(X > 0.42) = P(z > (0.42 - 0.3)/sqrt(0.3*0.7/78))

= P(z > 2.31)

= 0.0104441 [since from z table]

= 0.0104

c)

P(0.22 < X < 0.32) = P((0.22 - 0.3)/sqrt(0.3*0.7/78) < z < (0.32 - 0.3)/sqrt(0.3*0.7/78))

= P(- 1.54 < z < 0.39)

= P(z < 0.39) - P(z < - 1.54)

= 0.6517317 - 0.0617802 [since from z table]

= 0.58995