According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)

a. Compute the probability that a randomly selected peanut M&M is not red.



b. Compute the probability that a randomly selected peanut M&M is yellow or green.



c. Compute the probability that three randomly selected peanut M&M’s are all green.



d. If you randomly select five peanut M&M’s, compute that probability that none of them are orange.



e. If you randomly select five peanut M&M’s, compute that probability that at least one of them is orange.

7. The mean weekly earnings for employees in general automotive repair shops is $450 and the standard deviation is $50. A sample of 100 automotive repair employees is selected at random.
a. Find the probability that the mean earnings is less than $445.

b. Find the probability that the mean earning is between $445 and $455.

c.Find the probability that the mean earnings is greater than $460.

8. A drug manufacturer states that only 5% of the patients using a high blood pressure drug will experience side effects. Doctors at a large university hospital use the drug in treating 200 patients.
a.What is the probability that 15 or fewer patients will experience a side effect?

b. What is the probability that between 7 and 12 patients will experience a side effect?

8)   An airliner carries 150 passengers and has doors with a height of 75 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts​ (a) through​ (d).

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending. The probability is __________. ​(Round to four decimal places as​ needed.)

b. If half of the 150 passengers are​ men, find the probability that the mean height of the 75 men is less than 75 in. The probability is_______. ​(Round to four decimal places as​ needed.)

c. When considering the comfort and safety of​ passengers, which result is more​ relevant: the probability from part​ (a) or the probability from part​ (b)? Why? choose one

A. The probability from part​ (b) is more relevant because it shows the proportion of male passengers that will not need to bend.

B. The probability from part​ (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

C. The probability from part​ (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

D. The probability from part​ (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

d. When considering the comfort and safety of​ passengers, why are women ignored in this​ case? choose one

A. Since men are generally taller than​ women, it is more difficult for them to bend when entering the aircraft.​ Therefore, it is more important that men not have to bend than it is important that women not have to bend.

B. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.

C. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

An airliner carries

350

passengers and has doors with a height of

72

in. Heights of men are normally distributed with a mean of

69

in and a standard deviation of

2.8

in. Complete parts​ (a) through​ (d).

a. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

The probability is

nothing.

​(Round to four decimal places as​ needed.)

b. If half of the

350

passengers are​ men, find the probability that the mean height of the

175

men is less than

72

in.

The probability is

​(Round to four decimal places as​ needed.)

c. When considering the comfort and safety of​ passengers, which result is more​ relevant: the probability from part​ (a) or the probability from part​ (b)? Why?

A.

The probability from part​ (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

B.

The probability from part​ (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

C.

The probability from part​ (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

D.

The probability from part​ (b) is more relevant because it shows the proportion of male passengers that will not need to bend.

d. When considering the comfort and safety of​ passengers, why are women ignored in this​ case?

A.

There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.

B.

Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

C.

Since men are generally taller than​ women, it is more difficult for them to bend when entering the aircraft.​ Therefore, it is more important that men not have to bend than it is important that women not have to bend.

Assume that when an adult is randomly​ selected, the probability that they do not require vision correction is 28% If 12 adults are randomly​ selected, find the probability that fewer than 4 of them do not require a vision correction.

If 12 adults are randomly​ selected, the probability that fewer than 4 of them do not require a vision correction is ________

A binomial distribution has

pequals=0.550.55

and

nequals=4040.

A binomial distribution has p=0.550.55 and n=4040.

a. What are the mean and standard deviation for this​ distribution?

b. What is the probability of exactly 24 ​successes?

c. What is the probability of fewer than 27 ​successes?

d. What is the probability of more than19 ​successes?

1. How many 5 card poker hands are possible from a standard deck of cards?

2. What is the probability of a Royal Flush?

3. What is the probability of a Full House?

4. What is the probability of Two Pair?

5. How many more times likely is Two Pair than a Full House?   

A fair coin is flipped 80 times.
1) What is the probability that the first Tail is obtained sometime after the 20th coin flip
(include no tails)?
2) Find an exact expression for the probability that more than 40 Heads are obtained.
3) Find an approximate value for the probability in (2) using an appropriate Gaussian
approximation.