The percent of the parcels weighed between 12 ounces and 30 ounces will be 81.86%. And the percentage of the parcels weighing more than 42 ounces will be 0.13%
What is a normal distribution?
The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 24 ounces and a standard deviation of 6 ounces.
Then the percent of the parcels weighed between 12 ounces and 30 ounces will be
When x = 12, then we have
z = (12 - 24) / 6
z = -2
When x = 30, then we have
z = (30 - 24) / 6
z = 1
Then we have
P(12 < x < 30) = P(-2 < z < 1)
P(12 < x < 30) = 0.81859
P(12 < x < 30) = 81.86%
Then the percentage of the parcels weighing more than 42 ounces will be
When x = 42, then we have
z = (42 - 24) / 6
z = 3
Then we have
P(x > 42) = P(z > 3)
P(x > 42) = 1 - P(z < 3)
P(x > 42) = 0.0013499
P(x > 42) = 0.13%
More about the normal distribution link is given below.
https://brainly.com/question/12421652
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