Given a normal distribution with a mean of 128 and a standard deviation of 15, what percentage of values is within the interval
2 answers:
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Answer: See the picture attached.
Step-by-step explanation:
Given the following mixed numbers:
You need to convert them to decimal numbers. The steps to do this are shown below:
1. Divide the numerator of the fraction by the denominator.
2. Add the quotient obtained to the whole number part.
Then:
Therefore, the point is:
Where is the x-coordinate and
is the y-coordinate.
Knowing this, you can plot it on the coordinate plane, as you can see in the picture attached.
population mean, μ =135
population standard deviation, σ = 15
sample size, n = 19
Assume a large population, say > 100,
we can reasonably assume a normal distribution, and a relatively small sample.
The use of the generally simpler formula is justified.
Estimate of sample mean
Estimate of sample standard deviation
Thus, using the normal probability table,
Therefore
The probability that the mean weight is between 125 and 130 lbs
P(125<X<130)=0.0731166-0.0018308
=0.0712858