HW#2 – Introduction to the Normal Curve

1.(IN CLASS) Consider a probability density curve with height 1/5 from 0 to 4 and also from 19-20 and height 0 elsewhere. Draw the curve and estimate the mean and median. (note: its actually possible to find them both exact in this case.

2. Consider the following probability density curves. Tell for each which letter of A, B, and C is the mean and which is the median. Note there is no reason that the mean and median could not be the same.

graph (b) (SOLUTION GIVEN)

graph (a) (HOMEWORK)

graph (c) (ALTERNATE HW)

ACT math scores are roughly a normal distribution with mean 21.0 and standard deviation 4.7. SAT math scores are roughly a normal distribution with mean 515 and standard deviation 114.

3.(IN CLASS) Jerry scores 14 on the ACT math and Emily scores 395 on the SAT math. Assuming both tests measure the same thing, who has a higher score?

4. (ANSWER GIVEN) Maria scores 28 on the ACT math and Jimmy scores 660 on the SAT math. Assuming both tests measure the same thing, what score on the SAT is equivalent to Maria’s score?

5. (SOLUTION GIVEN) Jose scores 580 on the SAT math. Assuming both tests measure the same thing, what score on the ACT math is equivalent to Jose’s score?

6. (HOMEWORK) Tanya scores 530 on the SAT math and Natalie scores 22on the ACT math. Assuming both tests measure the same thing, who has the higher score?

7. (ALTERNATE HW) Sam scores 480 on the SAT math and Simon scores 19 on the ACT math. Assuming both test measure the same thing, who has the higher score?

8. (IN CLASS) Most people think that the average body temperature in adult humans is 98.6. However, this figure is based on data from the 1800’s. In a 1992 article in the Journal of the American Medical Association, it is reported a more accurate figure is 98.2. Assume a normal model is appropriate and that the standard deviation is 0.7.

A)In what range would you expect most people’s body temperatures to be?

B)What percentage of people would exceed 98.6?

C)What is the range for the coolest 20% of people?

D)What is the range for the hottest 10% of people?

E)What percentage of people would be below 98?

F)What percent will be between 98 and 99?

9. (ANSWER GIVEN) Suppose the measurements on the stress needed to break a type of bolt follow a Normal distribution with a mean of 75 kilopounds per square inch(ksi) and a standard deviation of 8.3 ksi.

A)What percent of these bolts will withstand a stress of 90ksi?

B)What range covers the middle 50% of breaking strengths?

C)What range of strengths are the 20% strongest?

D)What range of strengths are the 25% weakest?

E)What percent of these bolts will break with a stress of 80ksi?

F)What percent will be between 80 and 90?

10. (SOLUTION GIVEN) Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and standard deviation of 24.

A)What percent of adult women will have a cholesterol level over 200?

B)What percent of adult women will have a cholesterol level between 150 an 170?

C)What is the range for the middle 50%?

D)What is the range for the highest 15%?

E)What is the range for the lowest 25%?

F)What percent will be under 190?

11. (HOMEWORK) Biological measurements on the same species often follow a Normal distribution quite closely. The weights of seeds of a variety of winged bean are approximately Normal with a mean of 525 mg and a standard deviation of 110 mg.

A)What percent are over 500?

B)What is the range for the highest 10%?

C)What is the range for the lowest 5%?

D)What is the range for the middle 90%?

E)What percent are under 510?

F)What percent are between 500 and 600?

12. (ALTERNATE HW) Suppose the heights of women aged 20-29 follow approximately a Normal distribution with a mean of 64 inches and a standard deviation of 2.7 inches.

A)What percent of women are taller than the average man of the same age? (The average man of that age is 69.3 inches tall)

B)How tall are the tallest 5%?

C)How tall are the shortest 10%?

D)How tall are the middle 95%?

E)What percent are shorter than 60 inches?

F)What percent are between 63 inches and 69 inches?