Question

do the following question with a ti 84 and explain how you got your answers

currently quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.3 g. A vending machine if configured to accept only those quarters with weights between 5.550 g and 5.790 g

a) what is the probability of one quarter inserted into vending machine being accepted?

b) if 150 different quarters are inserted into vending machines, what is the probability that the mean falls between 5.550 g and 5.790 g.

c) if you own the vending machine, which result would concern you more? why?

Answer 1

Ans:

mean=5.670

standard deviation=0.3

a)Use Ti 84 command normalcdf:

P(5.550<X<5.790)=normalcdf(5.550,5.790,5.670,0.3)

=0.3108

b)standard error of mean=0.3/sqrt(150)=0.0245

P(5.550<X<5.790)=normalcdf(5.550,5.790,5.670,0.0245)

=1.0000

c)you should have more concern about result in part b,as probability of being accepted should be based on overall sample mean,individual quarter may have different weight largely.