Question

In: Statistics and Probability

The time required to assemble an electronic component is normally distributed with a mean and standard...

The time required to assemble an electronic component is normally distributed with a mean and standard deviation of 15 minutes and 8 minutes, respectively.

a. Find the probability that a randomly picked assembly takes between 12 and 19 minutes

b. It is an unusual for the assembly time to be above 28 minutes or below 5 minutes. What proportion of assembly times fall in these unusual categories?

Solutions

Expert Solution

µ = 15

sd = 8

a)

                                        

                                         = P(-0.38 < Z < 0.5)

                                         = P(Z < 0.5) - P(Z < -0.38)

                                         = 0.6915 - 0.3520

                                         = 0.3395

b)

                                                        

                                                         = P(Z > 1.63) + P(Z < -1.25)

                                                         = 1 - P(Z < 1.63) + P(Z < -1.25)

                                                         = 1 - 0.9484 + 0.1056

                                                         = 0.1572

Since the probability not less than 0.05, it is not unusual.

Th proportion is 0.1572

orchestra answered 1 year ago
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