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# Normal Distribution and Probability

1.The average weight of packages shipped by a courier company is 55 kg with a standard deviation of 20 kg. In a sample of 100 packages, what is the probability of getting a sample mean between 50 and 60 kg?
0.0062
0.4938
0.5000
0.9876

2.The scores for a group of high school students in a national physics examination were normally distributed with a mean of 86 and a standard deviation of 4. If there were 97,680 students with scores higher than 91, how may students sat for the examination?
161,295
247,667
925,000
976,800

3.A certain brand of floor lamps has a lifetime that is normally distributed with a mean of 3,750 hours and a standard deviation of 300 hours. What lifetime should the manufacturer advertise for these lamps given that approximately 2% of the lamps will burn out before the advertised lifetime?
3,050
3,132
3,150
3,675

#### Solution Preview

(1) M = 55, SD = 20, x1 = 50, x2 = 60, N = 100

z1 = (x1 - M)/(SD/sqrt N) = (50 - 55)/(20/sqrt 100) = -2.5

z2 = (x2 - M)/(SD/sqrt N) = (60 - 55)/(20/sqrt N) = 2.5

P(50 ...

#### Solution Summary

All the three problems solved in detail.

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