## Statistics-A large shipment of Granny Smith apples arrives at a grocery

(1)
A large shipment of
Granny Smith apples arrives at a grocery store. Weights of the apples are
known to follow a normal distribution with mean 152 grams and
standard deviation 16 grams.

(a) You select a random sample of three apples. Can you calculate
the probability that the mean weight of the apples in the sample is less
than 141.28?
(b) If you select a random sample of 40 apples, what is the
probability that the mean weight of the apples in the sample is
between 144.89 and 155.42?
(c) If you select a random sample of 50 apples, what is
the probability that the total weight of the apples is greater
than 7688.25 grams?
(d) Are the probabilities you calculated in (b) and (c) exact or
approximate? Explain.

(2)
The amount of a waiter’s tips follows some right-skewed
distribution with mean \$6.62 and standard deviation \$3.55.

(a) We take a random sample of three of the waiter’s customers. Can
you calculate the probability that the mean tip for these customers
is less than \$9.43?
(b) If we take a random sample of 35 of the waiter’s
customers, what is the probability that the mean tip for these customers
is greater than \$6.13?

(c) If we take a random sample of 45 of the waiter’s customers,
what is the probability that the mean tip for these customers is between
\$5.08 and \$6.87?
(d) Are the probabilities you calculated in (b) and (c) exact or
approximate? Explain.
(3)

A large lecture theater has 230 seats, 21 of which can
accomodate left-handed students. Suppose it is known that 12% of people
are left-handed. One class held in the theater
has 209 students.

(a) Let X be the number of left-handed students in the
class. What are the mean and standard deviation of X?

(b) Let.0/msohtmlclip1/01/clip_image001.gif” alt=”http://69.196.251.139/intellipro/geteq.ashx?eqtext=%40HAT%7Bp%7D”> be
the proportion of left-handed students in the class. What are the
mean and standard deviation of.0/msohtmlclip1/01/clip_image001.gif” alt=”http://69.196.251.139/intellipro/geteq.ashx?eqtext=%40HAT%7Bp%7D”>
?

(c) What is the approximate probability that all left-handed students in
the class get an appropriate desk?

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