The weights of adult Fox Terriers in US are normally distributed, with a mean of
ID: 3126374 • Letter: T
Question
The weights of adult Fox Terriers in US are normally distributed, with a mean of 15 pounds and a standard deviation of 3 pounds The probability that the randomly chosen Fox Terrier weighs between 9 pounds and 18 pounds is closest to 0.7961 0.2514 0.8185 0.0475 .9725 To be in the top 13% of the weights, a Fox Terrier should weigh at least 18.39 pounds 25.27 pounds 17.52 pounds 20.64 pounds 15 pounds A random sample of 100 Fox Terriersis drawn fom this population. Identify the mean mu_x and standard error sigma_x of the sample mean weight x mu_x=15, sigma_x = .3 x mu_x=1.5, sigma_x = 3 x mu_x=15, sigma_x = 3 x mu_x=15, sigma_x = 30 x mu_x=1.5, sigma_x = .3 Find the probability that the sample mean weight exceeds 16 pounds .996 .5000 .6293 .3707 .004Explanation / Answer
13.
We first get the z score for the two values. As z = (x - u) / s, then as
x1 = lower bound = 9
x2 = upper bound = 18
u = mean = 15
s = standard deviation = 3
Thus, the two z scores are
z1 = lower z score = (x1 - u)/s = -2
z2 = upper z score = (x2 - u) / s = 1
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.022750132
P(z < z2) = 0.841344746
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.818594614 [ANSWER, C]
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14.
First, we get the z score from the given left tailed area. As
Left tailed area = 1 - 0.13 = 0.87
Then, using table or technology,
z = 1.126391129
As x = u + z * s,
where
u = mean = 15
z = the critical z score = 1.126391129
s = standard deviation = 3
Then
x = critical value = 18.37917339 [ANSWER, A]
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15.
The mean remains the same, but the standard deviation is
sigma(X) = sigma/sqrt(n) = 3/sqrt(100) = 0.3
Hence,
OPTION A: ux = 15, sigma(X) = 0.3 [ANSWER, A]
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16.
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 16
u = mean = 15
n = sample size = 100
s = standard deviation = 3
Thus,
z = (x - u) * sqrt(n) / s = 3.333333333
Thus, using a table/technology, the right tailed area of this is
P(z > 3.333333333 ) = 0.00042906 [ANSWER, E]
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