The percentage of items will weight between 7.2 and 10.1 ounces is 89.29%
The mean of the weight in ounces = 9
The standard deviation of weights in ounces = 2
The percentage of items which will weigh between 7.2 and 10.1 can be calculated by normal distribution method,
P(7.2 < x < 10.1)
Let us find the standard form for these sample values using the formula,
Z =(X - μ) / σ
where Z is the standard form
X is the random sample
μ is the mean
σ is the standard deviation.
For x = 7.2 ,
Z = (7.2 - 9) / 2
= -1.8 / 2
= -0.9
For x = 10.1
Z = (10.1 - 9) / 2
= 1.1 / 2
= 0.55
Therefore P(7.2 < x < 10.1) = P(-0.9 < z < 0.55)
= P(-0.9 < z < 0) + P(0 < z < 0.55)
By using z-table , we can get the values of the z,
P(-0.9 < z < 0.55) = 0.18406 + 0.7088
= 0.89286
Therefore , the percentage of items will weight between 7.2 and 10.1
= 0.89286 x 100
= 89.29 %
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