Bolts produced by a machine are acceptable provided that their length is within
ID: 3131767 • Letter: B
Question
Bolts produced by a machine are acceptable provided that their length is within the range 5.95 to 6.0 oppose that the length of the bolts produced is normally distributed with mean of 6 inches and standard deviation of 0.2 inches. What is the probability that a randomly selected bolt will be of acceptable length? A theater makes a profit if they sell at least 800 tickets in a day. Suppose that the number of tickets sold day over the last year is normally distributed with mean 500 tickets and standard deviation 150 tickets What is the probability that the theater makes a profit on a randomly selected day? The mean for annual rainfall in Indianapolis is normally distributed with mean 50 inches and the deviation 5.5 inches. What is the probability that the annual rainfall will exceed 55 inches? What is the probability that the annual rainfall will be less than 30 inches? Assume that IQ scores arc normally distributed with a mean of 100 and a standard deviation of If people are identified for special education when their 10 score ,s m .he owes. population, what IQ score (to the nearest whole number) would a person need to What IQ score (to the nearest whole number) does 35 percentage of the population exceed?Explanation / Answer
10.
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 5.95
x2 = upper bound = 6.05
u = mean = 6
s = standard deviation = 0.2
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.25
z2 = upper z score = (x2 - u) / s = 0.25
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.401293674
P(z < z2) = 0.598706326
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.197412651 [ANSWER]
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11.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 800
u = mean = 500
s = standard deviation = 150
Thus,
z = (x - u) / s = 2
Thus, using a table/technology, the right tailed area of this is
P(z > 2 ) = 0.022750132 [ANSWER]
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