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NB: Use NORMDIST/MORMSDIST or NORM/NV/NORMSINV functions when solving this probl

ID: 3299538 • Letter: N

Question

NB: Use NORMDIST/MORMSDIST or NORM/NV/NORMSINV functions when solving this problem. Pick which funtion should e used.

An insurance company in country A sells policies to adult tourists who intend to visit the US for a period of less than three months. To limit its financial exposure, it requires interested customers to undertake a thorough physical examination and meet specified criteria for the different tests. One of the test results is blood pressure (BP). Historical records in country A indicate that adult systolic BP is normally distributed with a mean of 122mm of Hg and a standard deviation of 20mm. (BP is measured in millimeters of Mercury (Hg)).

a. If the company wants to deny policies to customers who are in the top 10% of BP values, at what value U should they set their upper cutoff ? (i.e. anyone with BP>U is denied coverage)

b. Having low blood pressure is also a health hazard, although not as serious as high pressure. So the company also wants to set a lower limit L on the BP test results. Anyone having a BP < L would be denied coverage. Where should they set the value of L so that the bottom 5% of BP values are denied coverage.

c. The current value of U is set by the company at 135. What percentage of applications will be denied as a result of this rule?

d. An executive at the company says that they can increase revenue by increasing U from 135 to 150. How much would revenues increase? Would you recommend making this change? Justify your answer

Explanation / Answer

a) mean = 122 , sd = 20

P(Z > z*) = 0.10

z* = 1.282

Z = (X - 122)/20

hence

X* = 122 + 20* 1.282 = 147.64

b)

P(Z < z* ) = 0.05

z* = -1.645

X* = 122 -1.645 * 20 = 89.1

c)

P(X > 135)

= P(Z >(135-122)/20)

=P(Z > 0.65)

=0.2578

hence 25.78%

d) P(135 < X< 150)

= P(0.65 <Z< 1.4)

=0.177