Sampling distribution for mu Birth weights for full-term babies is a normally di
ID: 3154279 • Letter: S
Question
Sampling distribution for mu Birth weights for full-term babies is a normally distributed random variable with a mean of 7.74 pounds and a standard deviation of 1.07 pounds. Normal distribution questions: If I pick 1 full-term baby, what is the probability that the birth weight is below 7 pounds? Suppose again I pick 1 full term baby. The middle 98% of these babies arc between what 2 weights? Sampling distribution questions: Suppose I pick a random sample of 32 babies. What is the probability that the sample mean for this date is below 7 pounds? Suppose I pick a random sample of 32 babies. The middle 98% of sample means are between what 2 values?Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 7
u = mean = 7.74
s = standard deviation = 1.07
Thus,
z = (x - u) / s = -0.691588785
Thus, using a table/technology, the left tailed area of this is
P(z < -0.691588785 ) = 0.244597803 [ANSWER]
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b)
As the middle area is
Middle Area = P(x1<x<x2) = 0.98
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.01
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -2.326347874
By symmetry,
z2 = 2.326347874
As
u = mean = 7.74
s = standard deviation = 1.07
Then
x1 = u + z1*s = 5.250807775
x2 = u + z2*s = 10.22919223
Hence, between 5.250807775 and 10.22919223 pounds. [ANSWER]
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c)
For 32 babies, the standard error would be
s(X) = s/sqrt(n) = 1.07/sqrt(32) = 0.189151064.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 7
u = mean = 7.74
s = standard deviation = 0.189151064
Thus,
z = (x - u) / s = -3.912216957
Thus, using a table/technology, the left tailed area of this is
P(z < -3.912216957 ) = 4.57263*10^-5 [ANSWER]
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d)
As the middle area is
Middle Area = P(x1<x<x2) = 0.98
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.01
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -2.326347874
By symmetry,
z2 = 2.326347874
As
u = mean = 7.74
s = standard deviation = 0.189151064
Then
x1 = u + z1*s = 7.299968824
x2 = u + z2*s = 8.180031176
Hence, between 7.299968824 and 8.180031176 lbs. [ANSWER]
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