Two causes of poor power quality are \"sags\" and \"swells.\" A sag is an unusua

Question

Two causes of poor power quality are "sags" and "swells." A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer. For transformers built for heavy industry, the mean number of swells per week was 192 with a standard deviation of 22 swells per week. The mean number of sags per week was 381 with a standard deviation of 28 sags per week. Assume that both the number of sags and the number of swells are normally distributed. Suppose one of the transformers is randomly selected and found to have 380 sags and 130 swells in a week.

a. What is the probability that the number of sags per week is less than 380?

b. What is the probability that the number of swells per week is greater than 130?

(Round to three decimal places as needed.)

Explanation / Answer

A) P(Sags< 380)

= P(X < 380)

= P(z < (380 - 381)/28)

= P(z < -0.04)

= 0.486

B) P(Swells > 130)

= P(X > 130)

= P(z > (130 - 192)/22)

= P(z > -2.82)

= 0.998

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