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Length of a machined part is known to have a normal distribution with a mean of 100mm and standard deviation of 2mm. What proportion of the parts will be shorter than 96.5mm? P(Z<-1.75)=0.0401 ops:="" a.="" 0.0401="" b.="" 0.0495="" c.="" 0.0583="" d.="" 0.0318?="" ops:="" a.="" 0.0401="" b.="" 0.0495="" c.="" 0.0583="" d.="">
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Length of a machined part is known to have a normal distribution with ...
Normal Distribution
Normal distribution is a probability distribution that is symmetrical and bell-shaped. It is characterized by its mean (µ) and standard deviation (σ).
Z-score
Z-score is a measure of the number of standard deviations a data point is from the mean. It is calculated by subtracting the mean from the data point and dividing the result by the standard deviation.
Solution
Given,
- Mean (µ) = 100mm
- Standard deviation (σ) = 2mm
- Length of the part (X) < />
We need to find the proportion of parts that will be shorter than 96.5mm. This can be found using the normal distribution table or calculator by converting the given value into a Z-score and finding its corresponding probability.
Using the Z-score formula,
Z = (X - µ) / σ
Z = (96.5 - 100) / 2 = -1.75
Using the normal distribution table, we can find the probability of Z being less than -1.75, which is 0.0401.
Therefore, the proportion of parts that will be shorter than 96.5mm is 0.0401 or 4.01%.
Hence, the correct option is A. 0.0401.
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Length of a machined part is known to have a normal distribution with a mean of 100mm and standard deviation of 2mm. What proportion of the parts will be shorter than 96.5mm? P(Z
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