Show all your work leading to the solutions. Work quickly but with care. Show es

Question

Show all your work leading to the solutions. Work quickly but with care. Show essential steps and formulas for "partial credit," and please use answer spaces where provided. Statistical Tables are attached (use the closest value if the exact number to check is not shown in the tables). (100 pts 20 x 5). 1. (20 pts) (A) A textbook has 600 pages on which typographical errors could occur. Suppose that there are exactly 12 such errors randomly located on those pages. (1) Find the probability that a random selection of 50 pages will contain no errors. (2) Find the probability that 50 randomly selected pages will contain at least two errors. (10 pts) B) The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard a) what must the standard deviation of weight be in order for company to state that 99.9% of its shoes are less b) If the standard deviation remains at 0.5 ounce, what must the mean weight be in order for the company to deviation of 0.5 ounce. (10 pts) than 13 ounces? state that 99.9% of its shoes are less than 13 ounces?

Explanation / Answer

A)

There are total 600 pages out of which 12 has errors.

1.
If 50 pages are selected from the remaining 588 non-erraneous pages, there will be no error

P(No error) = 588C50/600C50 = 0.3484

2.
P(Less than 2 errors) = P(No error) + P(1 error)
P(1 error) = 12C1*588C49/600C50 = 0.3879

P(Less than 2 errors) = 0.3484 + 0.3879 = 0.7363

Required probability = P(at least 2 errors) = 1 - 0.7363 = 0.2637

B)

mean = 12 , s = 0.5
a)
z value at 99.9% = -3.0902
x = 13

z = ( x - mean) / s
-3.0902 = ( 13 - 12)/s
s = 0.32

b)

z value at 99.9% = -3.0902
x = 13

z = ( x - mean) / s
-3.0902 = ( 13 - mean)/0.5
mean = 14.6
  

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