Question

1. If Y has a normal distribution with mean 116 and standard deviation 16, find P(Y < 87). Enter your answer as a decimal, not a percent. For example, if the answer is 0.3161, enter 0.3161, NOT 31.61%.

2.

It takes two days for a coffee shop to receive a shipment of milk from its supplier (this time is called "lead time" in operations management). During those three days, milk demand, Y, follows a normal distribution with a mean of 106.7 gallons and a standard deviation of 6.6 gallons. The coffee shop wants no more than a 7% (0.07 probability) of running out of milk before the shipment arrives. Find the point y at which the coffee shop should send in an order for milk, to one decimal place.

Hint: this is a "recover the original value" problem

QUESTION 10 Suppose Z is a standard normal random variable. Find the value of Ζα/2 such that P(-2α/2 SZ za/2)-0.80

Answer 1

Ans:

1)

z=(87-116)/16

z=-1.8125

P(z<-1.8125)=0.0350

2)P(Z<=z)=0.07

z=normsinv(0.07)=-1.476

x=106.7-1.476*6.6=97.0

3)

alpha=1-0.80=0.20

alpha/2=0.1

critical z value(two tailed)=normainv(0.1) or normainv(0.9)=1.282