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CJohnson9552
24.12.2019 •
Mathematics
Suppose you take a sample of 200 lehman students. the average height is 65 inches (5’4"") with a standard deviation of 5 inches. using the standard normal distribution: a) what would be the height in inches when the probability is 4.95% (0.0495) and when the probability is 95.05% (0.9505)? b) what would be the height if the probability is 99.01% (0.9901)?
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Ответ:
Step-by-step explanation:
Using the Standard Normal Distribution, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = height of students
u = mean score
s = standard deviation
From the information given,
n = 200
u = 65 inches
Standard deviation = 5 inches
a) when the probability is 4.95%. p = 0.0495
From the normal distribution table,
z = - 1.65
Therefore
- 1.65 = ( x- 65)/5
x - 65 = 5 × - 1.65 = - 8.25
x = -8.25 + 65 = 56.75 inches
The height is 56.75 inches
when the probability is 95.05%. p = 0.9505
From the normal distribution table,
z = 1.65
Therefore
1.65 = ( x- 65)/5
x - 65 = 5 × 1.65 = 8.25
x = 8.25 + 65 = 73.25 inches
The height is 73.25 inches
b) when the probability is 99.01%.
p = 0.9901
From the normal distribution table,
z = 2.33
Therefore
2.33 = ( x- 65)/5
x - 65 = 5 × 2.33 = 11.65
x = 11.65 + 65 = 76.65 inches
The height is 76.65 inches
Ответ:
it can be written as 4(p+q)