Homework SourseThe time required to assemble an electronic component is nor
The time required to assemble an electronic component is normally distributed with a mean and standard deviation of 24 minutes and 13 minutes, respectively. Use Table 1. a. Find the probability that a randomly picked assembly takes between 19 and 27 minutes. (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.) Probability b. It is unusual for the assembly time to be above 43 minutes or below 9 minutes. What proportion of assembly times fall in these unusual categories? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)
Solution
A)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 19
x2 = upper bound = 27
u = mean = 24
s = standard deviation = 13
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.38
z2 = upper z score = (x2 - u) / s = 0.23
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.352
P(z < z2) = 0.591
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.2390 [ANSWER]
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B)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 9
x2 = upper bound = 43
u = mean = 24
s = standard deviation = 13
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -1.15
z2 = upper z score = (x2 - u) / s = 1.46
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.1251
P(z < z2) = 0.9279
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.8028
Thus, those outside this interval is the complement = 0.1972 [ANSWER]
It is not unusual, because the probability is not less than 0.05.
