1. Use the table below to answer the following question:
| X |
1 |
2 |
3 |
4 |
5 |
Sums |
| P(X) |
0.17 |
0.19 |
0.16 |
0.05 |
0.43 |
|
| XP(X) |
|
|
|
|
|
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| X^2P(X) |
|
|
|
|
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a. Explain why the table "does" or "does not" form a probability distribution.
b. Find P(X is odd)
c. Complete row 3 of the table and find the mean for the random variable, "mu".
d. Complete row 4 of the table and find both variance, and standard deviation.
2. A recent study found that the fixed percentage listed below of a large population of frogs carry a gene for yellow speckled skin. 20.00%
a) A sample of six frogs is picked at random from this population.
Explain why it is reasonable or is not reasonable to consider X, the number of yellow speckled frogs in the sample, as a binomial random variable.
b) Use the formula for exact binomial probabilities to find P(X<4). Show all work.
c) Explain why normal approximation of the probabilities in parts a and b would or would not be appropriate.
d) Use the table I of appendix C to find the probability that a sample of 25 frogs from this population has the following number of yellow speckled specimens.
e) For this larger sample of 25 frogs, would normal approximation be appropriate? Explain why or why not.
f) Regardless of your answer for part e. find the normal approximation for the same probability found in part d. Don't forget to use continuity correction. Indicate mean and standard deviation, as well as value of Z used. Show ALL work'
3. Past extensive study of the athletic long jumping capabilities for yellow speckled frogs has found the mean arm standard deviation for the population to be as listed below.
mean 80 cm
standard deviation 6 cm
a) If the jump lengths are NOT assumed to follow any known distribution, then explain why normal calculation would or %you'd not be appropriate.
b) Regardless of your answer to part a) find probability that a randomly selected frog from the population has a jump between 40 and 50 cm.
c) What jump lengths corresponds to the top notch jumpers using the percentage 20.00%.
d) A sample of the following size is drawn. n = 49
Find probability of a sample mean less than: 71 cm
Does it matter whether the random variable for jump length is normal when finding probabilities related to these sample means? Why or why not?
e) Find the range of values corresponding the middle percentage listed (40.00%) for samples of size matching part d.