HW #22 – Binomial Probability and Normal Distribution Revisited

1. (IN CLASS) The number of people in cars driving on North Avenue is not normally distributed, in fact it is not even continuous (its discrete). Suppose the mean is 1.8 and the standard deviation is 1.1.

A) If 60 cars are picked at random, what is the probability that the average number of people is more than 2?

B) Only 10% of sample means of samples of size 60 will be above what number?

2. (ANSWER GIVEN) Roll 40 dice repeatedly and find the average number of pips per dice. If one die is rolled the mean is 3.5 and the standard deviation is 1.708. Also note that for one die the number of pips is not normally distributed.

A) What is the probability that on one time when 40 are rolled the average number of pips will exceed 4?

B) Only 5% of the time the 40 dice will have an average higher than what number?

3. (SOLUTION GIVEN) Suppose the average number of customer’s in the checkout line at a grocery store is 2.5 with a standard deviation of 1.8. Note that the number of customer’s in line is not normally distributed.

A) What is the probability that the average number of customers in line in a random sample of 50 checkout lines is over 3?

B) In only 1% of samples of size 50 will the average number of customers in line exceed what number?

4. (HOMEWORK) The number of accidents at a busy intersection in one month is not normally distributed, but has a mean of 2.8 and a standard deviation of 2.1.

A) If 55 months are studied at random what is the probability the average number of accidents will exceed 3?

B) There is only a 1% chance the average of 55 months picked at random will exceed what number?

5. (ALTERNATE HW) The number of speeding tickets per day given by a certain police officer is not normal, but has a mean of 5.2 and a standard deviation of 3.2.

A) If 66 days are picked at random, what is the probability the average number of speeding tickets will exceed 6?

B) There is only a 5% chance the average over 66 days will exceed what number?

6. (IN CLASS) Suppose 62% of households in a certain city own a foreign car.

A) What is the probability that in a sample of 10 households that exactly 8 will own a foreign car?

B) What is the probability that in a sample of 10 households that 8 or less will own a foreign car?

C) What is the mean number of households that own a foreign car in samples of size 120?

D) What is the standard deviation of the number of households that own a foreign car in samples of size 120?

E) What is the probability that in a sample of size 120 that 80 or more households will own a foreign car?

7. (ANSWER GIVEN) Suppose 14% of prairie dogs in an area carry bubonic plague.

A) What is the probability that in a sample of 15 prairie dogs that exactly 2 will carry bubonic plague?

B) What is the probability that in a sample of 15 prairie dogs that more than 2 will carry bubonic plague?

C) What is the mean number of prairie dogs that carry bubonic plague in samples of size 150?

D) What is the standard deviation of the number of prairie dogs that carry bubonic plague in samples of size 150?

E) What is the probability that in a sample of size 150 that 20 or less will carry bubonic plague?

8. (SOLUTION GIVEN) Suppose in a certain country that 22% of men are taller than 6 foot tall.

A) What is the probability that in a sample of 18 men that exactly 2 will be over 6 foot tall?

B) What is the probability that in a sample of 18 men that more than 2 will be taller than 6 foot tall?

C) What is the mean number of men that will be taller than 6 foot in samples of size 180?

D) What is the standard deviation of the number of men that will be taller than 6 foot in samples of size 180?

E) What is the probability that in a sample of size 180 that 44 or less will be taller than 6 foot?

9. (HOMEWORK) Suppose a hidden camera at a residential intersection with a stop sign is put up and it is found that only 17% of cars actually completely stop at the stop sign.

A) What is the probability that in a sample of 16 cars that exactly 2 will completely stop?

B) What is the probability that in a sample of 16 cars that more than 2 will completely stop?

C) What is the mean number of cars that will completely stop in samples of size 120?

D) What is the standard deviation of the number of cars that will completely stop in samples of size 120?

E) What is the probability that in a sample of size 120 that 20 or less will completely stop?

10. (ALTERNATE HW) Suppose in world class track meets that there is a false start in 24% of 100 meter races.

A) What is the probability that in a sample of 10 races that exactly 3 will have false starts?

B) What is the probability that in a sample of 10 races that more than 3 will have false starts?

C) What is the mean number of races that will have false starts in samples of size 90?

D) What is the standard deviation of the number of races that will have false starts in samples of size 90?

E) What is the probability that in a sample of size 90 that 20 or less will have false starts?