Assume that women\'s heights arc normally distributed with a mean given by Mu -
ID: 3386698 • Letter: A
Question
Assume that women's heights arc normally distributed with a mean given by Mu - 63.8 in, and a standard deviation given by sigma = 2.6 in. (a) If 1 woman is randomly selected, find the probability that her height is between 63.4 in and 64.4 in The probability is approximately [ ] . (Round to tour decimal places as needed.) (b) If 11 women an randomly selected, find the probability that they have a mean height between 63.4 a sad 64.4 in. The probability is approximately [ ] . (Round to four decimal plates as needed.) (c) Why can the central limit theorem be used in part (b), even though the maple site does not exceed 30? A The sample site needs to be less than 30, not greater than 30. B. The population size is greater than 30. D. The sample is normally distributed. E The population a normally distributed.Explanation / Answer
a)
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 63.4
x2 = upper bound = 64.4
u = mean = 63.8
s = standard deviation = 2.6
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -0.153846154
z2 = upper z score = (x2 - u) / s = 0.230769231
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.438865521
P(z < z2) = 0.591252957
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.152387436 [ANSWER]
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b)
We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as
x1 = lower bound = 63.4
x2 = upper bound = 64.4
u = mean = 63.8
n = sample size = 11
s = standard deviation = 2.6
Thus, the two z scores are
z1 = lower z score = (x1 - u) * sqrt(n) / s = -0.510249968
z2 = upper z score = (x2 - u) * sqrt(n) / s = 0.765374952
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.304938175
P(z < z2) = 0.777975848
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.473037673 [ANSWER]
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c)
OPTION D: The population is normally distributed.