Normal?t
and Binomial Distributions

Assume that women's height are
normally distributed with a mean given by =63.4 in, and a standard deviation
given by =2.7in.

If 1 woman is randomly selected,
find the probability that her height is less than 64 in.

If 46 women are randomly selected
find the probability that they have a mean height less than 64 in.

Cans of a certain beverage are
labeled to indicate that they contain 8oz. The amounts in a sample of cans are
measured and the sample statistics are n=44 and x=8.04oz. If the beverage cans
are filled so that µ=8.00 oz (as labeled) and the population standard
deviations is ?=0.107 oz (based on the sample results), find the probability
that a sample of 44 cans will have a mean of 8.04 oz or greater. Do these
results suggest that the beverage cans are filled with an amount greater than
8.00 oz?

The probability that a sample of
44 cans will have a mean of 8.04 oz or greater, given that µ =8.00 and ?
=0.107, is____

(a) With n=11 and p=0.6, find the
binomial probability P(5) by using a binomial table. (b) If np ? 5 and nq ? 5,
also estimate the indicated probability by using the normal distribution as an
approximation to the binomial; if np < 5 or nq < 5, then state the normal
approximation cannot be used.

Find the probability by using a
binomial probability table.

P(5)=___(round 3 decimal places as
needed)

Assume the readings on
thermometers are normally distributed with a mean of 0 C and a standard
deviation of 1.00 C. Find the probability that a randomly selected thermometer
reads less than 0.13 and draw a sketch of the region.

a) If the random variable z is the
standard normal score and a>0, is it true that P (z<-a)= P(z>a)? Why
or why not?

b) Find the z-score for the
standard normal distribution where Area=0.32 in the left trail.