## 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?

**CLICK HERE TO ORDER A SIMILAR PAPER**

We pride ourselves in writing quality essaysCLICK HERE TO CONTACT US