Homework SourseThe credit scores of 35yearolds applying for a mortgage at U
The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 670 and a standard deviation of 125.
(Round to 2 decimal places).
(a)
Find the credit score that defines the upper 15 percent.
(b)
Fifty-five percent of the customers will have a credit score higher than what value?
(c)
Within what range would the middle 60 percent of credit scores lie?
Solution
a)
Here, the left tailed area is 1-0.15= 0.85.
First, we get the z score from the given left tailed area. As
Left tailed area = 0.85
Then, using table or technology,
z = 1.036433389
As x = u + z * s,
where
u = mean = 670
z = the critical z score = 1.036433389
s = standard deviation = 125
Then
x = critical value = 799.5541737 [ANSWER]
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b)
Here, the left tailed area is 1-0.55= 0.45.
First, we get the z score from the given left tailed area. As
Left tailed area = 0.45
Then, using table or technology,
z = -0.125661347
As x = u + z * s,
where
u = mean = 670
z = the critical z score = -0.125661347
s = standard deviation = 125
Then
x = critical value = 654.2923316 [ANSWER]
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c)
Note that
Lower Bound = X - z(alpha/2) * s
Upper Bound = X + z(alpha/2) * s
where
alpha/2 = (1 - confidence level)/2 = (1-0.60)/2 = 0.2
X = sample mean = 670
z(alpha/2) = critical z for the confidence interval = 0.841621234
s = sample standard deviation = 125
Thus,
Lower bound = 564.7973458
Upper bound = 775.2026542
Thus, the confidence interval is
( 564.7973458 , 775.2026542 ) [ANSWER]
