QUESTION 1 A person takes part in a medical trial that tests the effect of a medicine on a disease. Half the people are

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QUESTION 1
A person takes part in a medical trial that tests the
effect of a medicine on a disease. Half the people are given
medicine and the other half are given a sugar pill, which has no
effect on the disease. The medicine has a 60% chance of curing
someone. But people who do not get the medicine still have a 10%
chance of getting well. There are 50 people in the trial, and they
all have the disease. John takes part in the trial, but we do not
know whether he got the medicine or the sugar pill.
QUESTION 2
The machines used to fill detergent bottles in a
detergent industry do not always fill the bottles to specification.
In this industry, a machine may: A, fill to specification; B,
underfill, or C, overfill. Let P(B) = 0.001 while P(A) =
0.990.
(a) Give P(C).
(b) What is the probability that the machine does not
underfill?
(c) What is the probability that the machine either
overfills or underfills?
QUESTION 3
A machine produces parts with lengths that are normally
distributed with σ= 0.5 cm. A sample of 10 parts was found to have
a mean length of 75.92 cm. Find the 95% confidence interval
for the population mean, μ, of all parts produced by this
machine.