Suppose the time needed to assemble a particular gizmo has a

Suppose the time needed to assemble a particular gizmo has a bell-shaped distribution. The mean assembly time is 125 minutes and the standard deviation is 12 minutes.

1) What percentage of the gizmos are assembled between 101 and 149 minutes?

2) Between what two assembly times would approximately 68% of the values fall?

Solution

1)

As we see, 101 and 149 are both 2 standard deviations away from the mean of 125 minutes.

Hence, by 68-95-99.7 rule, we know that the answer is 95%. [ANSWER]

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2)

By the 68-95-99.7 rule, those within 1 standard deviation from the mean make up 68% of the values.

Hence, they are between 125 - 12 and 125 + 12, or

between 113 and 137. [ANSWER]