Probability function and distribution

(See attached file for full problem description)

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1. Given the probability function P(x)=(2x-1)/16, for x=1,2,3,4.
a. Write the probability distribution:
b. Find the U (pop. mean)
c. Find the O (pop. SD)

2. The number of cars to be worked on by a mechanic at ABC garage is a random represented x. The probability distibution is:
x 25 26 27 28 29
P(X).17 .18 .35 .25 .05
Find the probability that on a given day a mechanic works on :
a. exactly 28 cars
b. at least 27 cars
c. at most 27 cars
d. find the mean number of cars worked on:
e. find the standard deviation:

3. Fins the mean & standard deviation of the following probability distibution:
x 10 13 15 16 18
p(x) 1/12 1/4 1/3 1/6 1/6

a. Mean:
b. Standard Deviation:

4. Find the following probabilities:
a. p(z<1.78)
b. p(z>1.68)
c. p(-1.48<Z<1.55)
d. p(z>-1.29)
f. p(-2.52<Z<-1.74)

5. The middle 85% of a normally distributed population falls between what 2 standard scores?

6. The length of life of a certain type of wash machine is approximately normally distributed with a mean of 4.6 yrs. and a SD of 0.8 yrs. If the machine is guaranteed for 2 years, what is the probability that replacement, while under guarantee, will be required?

7. Scores on a college entrance exam are normally distributed with a mean of 570 and SD of 80. A college gives priority acceptance to those scoring above 680. What % of subjects are eligible for priority acceptance?

8. The weights of women aged 18 to 24 are normally distributed with a mean of 128# and SD of 20.8#. If 150 women are randomly selected, how many would you expect to weigh between 120 and 145?

9. A particular dexterity test is administered nationwide by a private testing service. The mean is 78, SD of 9.5, and normally distributed.
a. A particular employer requires candidates to score at least 80 on the test. What % of the test scores exeeded 80?
b. The testing service reported to a particular employer that the score of one of it's job candidates fell at the 35th percentile. What was the candidates score?

10. On average, 3% of the boards purchases by a cabinet manufacturer are unusable.
a. What is the probability that 7 or less out of a set of 14 are usable?
b. What is the expected # of unusable boards?
c. What is the SD of the distribution?
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