In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 69.7 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below.
​(a) Find the probability that a study participant has a height that is less than 65 inches.
The probability that the study participant selected at random is less than 65 inches tall is
. 0094. ​(Round to four decimal places as​ needed.)
​(b) Find the probability that a study participant has a height that is between 65 and 70 inches.
The probability that the study participant selected at random is between 65 and 70 inches tall is
nothing. ​(Round to four decimal places as​ needed.)
​(c) Find the probability that a study participant has a height that is more than 70 inches.
The probability that the study participant selected at random is more than 70 inches tall is

The table gives percentages for results of flipping six coins. Complete parts (a) through (c) below.

a. What is the probability that all six tosses are the same (all heads or tails)?

The probability is________ (simplify your answer)

b. What is the proability that the six tosses are not all the same?

The probability is ________(simplify your answer)

c. What is the probability of getting two heads and four tails when you toss six coins at once?

The probability is________(simplify your answer)

Result                                               Probability

0 heads, 6 tails                                  1/64

1 head, 5 tails                                     3/32

2 heads, 4 tails                                   15/64

3 heads, 3 tails                                      5/16

4 heads, 2 tails                                15/64

5 heads, 1 tail                                3/32

6 heads, 0 tails                             1/64

	Fatal (L1)	Non Fatal(L2)	Survival(L3)
Russia (C1)	9	56	13
Brazil (C2)	12	21	39
United States (C3)	8	57	7
South Africa (C4)	5	244	16

Following is a contingency table providing a cross-classification of worldwide reported shark attacks during the 1990s, by country and lethality of attack.

1. Find the probability that the attack was Nonfatal
2. Find the probability that Brazil reported
3. Find the probability that Brazil reported the attack was Nonfatal
4. Find the probability that Brazil reported or the attack was Nonfatal
5. Find the probability that Brazil reported given that the attack was Nonfatal
6. Find the probability that the attach was Nonfatal given that Brazil reported
7. Construct a Relative Frequency Contingency Table, determine parts (i-vi) again
8. Verify your answers obtained from contingency table and relative frequency contingency table

5) A lumber grading system is known to be defective 20% of the time. When the machine works properly, 20% of the lumber that passes through is rejected, but 50% of the pieces are rejected when it is defective,. In either case, pieces that are accepted are graded this way:

20% #1 Grade

70% #2 Grade

10% #3 Grade

a. Draw a tree diagram outlining each possible outcome. Include all of the

relevant probabilities as well as the probability for each outcome.

b. What is the overall probability of accepting a piece of lumber?

c. What is the overall probability of getting a #2 Grade piece?

d. What is the probability of accepting a piece of lumber if you know that the machine is working properly?

e. What is the probability that a piece that was rejected came from a defective machine?

f. What is the probability that a piece that was rejected came from a working machine?

Hannah coaches a youth soccer team . Tomorrow night, they have a game. Suppose there is a 43% chance that her team will lose. Regardless of whether her team loses, Hannah figures there is a 58% chance that a parent will complain about something to her after the game. From previous seasons, Hannah knows that the probability that her team loses and a parent complains is 35%.  (Hint: Organize and label the given information first before starting. Write out the probability statement for each question before calculating anything.)

(Round all probabilities to four decimals)

1. Suppose Hannah’s soccer team loses. What is the probability that a parent complains?

2. If a parent complains after the game, what is the probability that Hannah’s team lost?

3. What is the probability that Hannah’s team will win tomorrow night?

4. Suppose Hannah’s soccer team loses. What is the probability that a parent does not complain?

Alex has two funds A and B. The annual return of fund A is denoted by X (in %) while the annual return of fund B is denoted by Y (in %) . Assume X ∼ U (−10, 20) and Y ∼ N (10, 50). Further, suppose the probability that both stocks A and B have positive annual returns is 0.6.

1. Find the probability that stock A has a negative return.

2. Find the probability that stock B has a positive return.

3. Find the probability that stock B has a positive return but stock A has a negative return.

4. Find the probability that stock A has a negative return, given that stock B has a positive return.

5. Find the probability that both stocks A and B have negative returns.

I would appreciate if the expert can write down some explanations for the more complicated steps so that I can understand how they derive that step. Thanks!

Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu = 283 days and standard deviation sigma = 29 days. (a) What is the probability that a randomly selected pregnancy lasts less than 273 days? The probability that a randomly selected pregnancy lasts less than 273 days is approximately (Round to four decimal places as needed.) (b) What is the probability that a random sample of 11 pregnancies has a mean gestation period of 273 days or less? The probability that the mean of a random sample of 11 pregnancies is less than 273 days is approximately (c) What is the probability that a random sample of 42 pregnancies has a mean gestation period of 273 days or less? The probability that the mean of a random sample of 42 pregnancies is less than 273 days is approximately (Round to four decimal places as needed.)

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

a.	What is the probability that you will receive a Merit scholarship? Hint: P(M∪A) = P(M) + P(A) – P(M∩B)
b.	Are events A and M mutually exclusive? Why or why not? Explain.
c.	Are the two events A, and M, independent? Explain, using probabilities.
d.	What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? Hint: P(A|M) = P(A∩M)/P(M)
e.	What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship? Hint: P(M|A) = P(M∩A)/P(A)

One college class had a total of 70 students. The average score for the class on the last exam was 84.2 with a standard deviation of 4.8. A random sample of 31 students was selected. a. Calculate the standard error of the mean. b. What is the probability that the sample mean will be less than 86​? c. What is the probability that the sample mean will be more than 85​? d. What is the probability that the sample mean will be between 83.5 and 85.5​? a. The standard error of the mean is nothing. ​(Round to two decimal places as​ needed.) b. The probability that the sample mean will be less than 86 is nothing. ​(Round to four decimal places as​ needed.) c. The probability that the sample mean will be more than 85 is nothing. ​(Round to four decimal places as​ needed.) d. The probability that the sample mean will be between 83.5 and 85.5 is nothing. ​(Round to four decimal places as​ needed.)