SOLUTION: 1).a set of 50 data values has a mean of 40 and a variance of 25. a). Find the standard score (z) for a data value = 47. b). Find the probability of a data value >47.

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Question 362457: 1).a set of 50 data values has a mean of 40 and a variance of 25.
a). Find the standard score (z) for a data value = 47.
b). Find the probability of a data value >47.

(2). Find the area under the standard normal curve:
I. to the right of z = 1.83
II. to the left of z = 1.83

Found 3 solutions by stanbon, ewatrrr, sunsetatdawn:
Answer by stanbon(75887)   (Show Source):
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1).a set of 50 data values has a mean of 40 and a variance of 25.
a). Find the standard score (z) for a data value = 47.
z(47) = (47-40)/25 = 0.28
b). Find the probability of a data value > 47.
P(x> 47) = P(z > 0.28) = 0.3897
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(2). Find the area under the standard normal curve:
I. to the right of z = 1.83
P(z > 1.83) = 0.0336
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II. to the left of z = 1.83
P(z < 1.83) = 1-0.0336 = 0.9664
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Cheers,
Stan H.

Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!

Hi,
(2). Find the area under the standard normal curve:
I. to the right of z = 1.83 (1 - area to the left)
.034 represents the area under the standard normal curve to the right of blue line
II. to the left of z = 1.83
.966 represents the area under the standard normal curve to the left of blue line

Answer by sunsetatdawn(4)   (Show Source):
You can put this solution on YOUR website!
The answer to #1 I don't think is quite right. We are supposed to divide by standard deviation, not variance. To get this, find the square root of the variance.
so it is more like this (47 - 40)/sqrt25 = 7/5 = 1.4