The annual sales or a large company is uniformly distributed from Php 500.000 to

Question

The annual sales or a large company is uniformly distributed from Php 500.000 to Php 800.000. At Php 600.000 the company breaks even A turning the peso sales is measured to any degree of accuracy. What is the probability that the company makes a profit? What is the probability that sales is between Php 650,000 and Php 750,000? What would be the expected annual peso sales? A train arrives at a station every hour between 1:00p.m. and 9:00p.m. What is the probability that a man entering the station between 1:00p.m. and 2:00p.m. will have to wait for at least 15 minutes? The distribution of personal daily water usage in a large city is uniformly distributed with a mean of 20 gallons and a variance of 4. What is the probability that at least 18 gallons is used in a particular day? at least 18 is used for 2 days in a particular week? The heights of engineering students arc normally distributed with a mean of 64 inches and a standard deviation of 6 inches. What is the probability that an engineering student selected will have a height of less than 62 inches? more than 62 inches? between 55.2 and 71.3 inches? The quality control manager shuts down an automatic lathe for corrective maintenance whenever a sample of parts it produces has an average diameter either exceeding 2.01 inches or smaller than 1.99 inches. The lathe is designed to produce parts with a mean diameter of 2.00 inches and a standard deviation of 0.005 inches. Assuming normality,

Explanation / Answer

a) Prob company makes a profit

= Prob (production > Break even)

= 2/3 =0.667

b) P(650000<x<750000) = 1/3 =0.333

c) Expected sales = (500000+800000)/2=650000

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Average train per hour = 1

Hence avg for 15 minutes = 0.25

P(X=0 when Poisson avg = 0.25) = 0.7788

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20) P(X>18) = 2/20 = 0.1

For 2 days 18 mean 1 day 9

Hence P(X>9) = 11/20 =0.55

21) mu - 64 and sigm a=6

a) P(X<62) = P(Z<-1/3) = 0.3707

b) P(X>62) = 1-0.3707 =0.6293

c) P(55.2<X<71.3) = P(-1.13<z<1.22)=0.3708+0.3888

= 0.7596

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