Homework SourseA The lengths of time bank customers must wait for a teller
A. The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute.
1.What proportion of bank customers waits between 3 and 4.5 minutes
2. What percentage wait more than 4 minutes?
3.What proportion waits between 2 and 3.5 minutes?
4. What percentage wait less than 1 minute?
B. A review of the records at Lander Community College revealed the following ethnic breakdown of the student population:
Caucasian 1200
Black 640
Hispanic 280
Asian 80
Native American 60
Other 20
1.What is the probability that a randomly selected student is either Caucasian or Black?
2.What is the probability that the selected student is not a member of either of the two largest categories?
Solution
1.What proportion of bank customers waits between 3 and 4.5 minutes
P(3<X<4.5) = P((3-3)/1 <(X-mean)/s <(4.5-3)/1)
=P(0<Z<1.5) = 0.4332 (from standard normal table)
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2. What percentage wait more than 4 minutes?
P(X>4) = P(Z>(4-3)/1)
=P(Z>1) =0.1587 (from standard normal table)
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3.What proportion waits between 2 and 3.5 minutes?
P(2<X<3.5) = P((2-3)/1<Z<(3.5-3)/1)
=P(-1<Z<0.5) =0.5328 (from standard normal table)
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4. What percentage wait less than 1 minute?
P(X<1) = P(Z<(1-3)/1)
=P(Z<-2) = 0.0228 (from standard normal table)
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1.What is the probability that a randomly selected student is either Caucasian or Black?
(1200+640)/(1200+640+280+80+60+20)= 0.8070175
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2.What is the probability that the selected student is not a member of either of the two largest categories?
1-0.8070175 =0.1929825
