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# Normal probability calculation

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#1
The average number of customer complaints at the Full Moon Motel is five per day.
Find the probability that on a typical day, the motel will receive

a) eight complaints
b) at least two complaints

#2
Demand for a product is normal, with mean being 400 and standard deviation being 25 units. Find

a) Pr (demand > 445)
b) Pr (demand is between 375 and 425)
c) Pr (demand equals 400)
d) Pr (demand exceeds 500)
e) The 5 percentile demand level

#3The sales of a product are uniformly distributed between 300 and 800. Find

a) Probability (Sales < 500)
b) Probability (Sales between 700 and 900)
c) Probability of sales exactly equal to 750
d) 15 percentile sales level

https://brainmass.com/statistics/probability-density-function/normal-probability-calculation-142214

#### Solution Preview

#1 The average number of customer complaints at the Full Moon Motel is five per day.
Find the probability that on a typical day, the motel will receive

a) Eight complaints
b) At least two complaints
Let X be the number of complaints at the Full Moon Motel. Given that X is Poisson with mean  = 5. The probability density function of Poisson random variable is given by
The probabilities for different values of X are given below

X P(X=x)
0 0.006737947
1 0.033689735
2 0.084224337
3 0.140373896
4 0.17546737
5 0.17546737
6 0.146222808
7 0.104444863
8 0.065278039
9 0.036265577

a). P(X=8) = 0.065278039
b). ...

#### Solution Summary

This solution gives the step by step method for computing probability from normal distribution.

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