1. Find z (a standardized score), given the following. (Give your answer correct
ID: 3131691 • Letter: 1
Question
1. Find z (a standardized score), given the following. (Give your answer correct to two decimal places.)
x = 246, = 215 and = 11.6
z =
2. Final averages are typically approximately normally distributed with a mean of 72 and a standard deviation of 10. Your professor says that the top 8% of the class will receive an A; the next 24%, a B; the next 36%, a C; the next 20%, a D; and the bottom 12%, an F. (Give your answers correct to one decimal place.)
(a) What average must you exceed to obtain an A?
(b) What average must you obtain to pass the course? (You'll need a D or better.)
Explanation / Answer
1.
As
z = (x-u)/sigma
Then
z = (246-215)/11.6 = 2.672413793 [ANSWER]
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2.
a)
First, we get the z score from the given left tailed area. As
Left tailed area = 1 - 0.08 = 0.92
Then, using table or technology,
z = 1.40507156
As x = u + z * s,
where
u = mean = 72
z = the critical z score = 1.40507156
s = standard deviation = 10
Then
x = critical value = 86.05071 = 86.1 [ANSWER]
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B)
You should not be on the bottom 12%, then.
First, we get the z score from the given left tailed area. As
Left tailed area = 0.12
Then, using table or technology,
z = -1.174986792
As x = u + z * s,
where
u = mean = 72
z = the critical z score = -1.174986792
s = standard deviation = 10
Then
x = critical value = 60.25013208 = 60.3 [ANSWER]
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