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 180 with a standard deviation of 21.8 swells per week. The mean number of sags per week was 330 with a standard deviation of 25 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 410 sags and 90 swells in a week.   a. What is the probability that the number of sags per week is less than 410​? b. What is the probability that the number of swells per week is greater than 90​? a. The probability that the number of sags per week is less than 410 years is nothing. ​(Round to three decimal places as​ needed.)

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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
180
with a standard deviation of
21.8
swells per week. The mean number of sags per week was
330
with a standard deviation of
25
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
410
sags and
90
swells in a week.
 
a. What is the probability that the number of sags per week is less than
410​?
b. What is the probability that the number of swells per week is greater than
90​?
a. The probability that the number of sags per week is less than
410
years is
nothing.
​(Round to three decimal places as​ needed.)
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