Question

The average amount of money that people spend at McDonalds fast food place is $7.4000 with a standard deviation of $1.6700. 11 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.

A.)What is the distribution of X? X ~ N()

B.)What is the distribution of ¯x? ¯x ~ N()

C.)What is the distribution of ∑x? ∑x ~ N(,)

D.)What is the probability that one randomly selected customer will spend more than $7.4148?

E.)For the 11 customers, find the probability that their average spent is more than $7.4148.

F.)Find the probability that the randomly selected 11 customers will spend more than $81.5628.

G.)For part e) and f), is the assumption of normal necessary? No or Yes

H.)The owner of McDonalds gives a coupon for a free sundae to the 4% of all groups of 11 people who spend the most money. At least how much must a group of 11 spend in total to get the free sundae? $

Answer #1

**Answer:**

Given,

Mean = 7.4

Standard deviation = 1.67

Sample = 11

a)

X ~ N(7.4 , 1.67)

b)

Xbar ~ N(7.4 , 1.67/sqrt(11)) ~ N(7.4 , 0.50)

c)

∑x ~ N(7.4*11 , sqrt(11)*1.67) = ∑x ~ N(81.4 , 5.54)

d)

P(X > 7.4148) = P(z > (7.4148 - 7.4)/1.67)

= P(z > 0.01)

= 0.4960106 [since from z table]

= 0.4960

e)

P(Xbar > 7.4148) = P(z > (7.4148 - 7.4)/0.50)

= P(z > 0.03)

= 0.4880335 [since from z table]

= 0.4880

f)

P(∑X > 81.5628) = P(z > (81.5628 - 81.4)/5.54)

= P(z > 0.03)

= 0.4880335 [since from z table]

= 0.4880

g)

Yes

h)

P(∑x > x) = 0.04

P(z > (x - 81.4)/5.54) = 0.04

since from z table

(x - 81.4)/5.54 = 1.755

x = 91.1227

The average amount of money that people spend at Don Mcalds fast
food place is $7.3800 with a standard deviation of $1.6900. 48
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution. What is the distribution of X X ?
X X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What
is the distribution of ∑ x...

The average amount of money that people spend at Don Mcalds fast
food place is $7.2000 with a standard deviation of $1.5000. 15
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
What is the probability that one...

The average amount of money that people spend at Don Mcalds fast
food place is $7.7000 with a standard deviation of $1.8900. 46
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
What is the probability that one...

The average amount of money that people spend at Don Mcalds fast
food place is $7.7500 with a standard deviation of $1.7200. 48
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution. What is the distribution of X ? X
~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) What is the
distribution of ∑ x...

The average amount of money that people spend at Don Mcalds fast
food place is $7.7500 with a standard deviation of $1.7200. 48
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution. What is the distribution of X ? X
~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) What is the
distribution of ∑ x...

The average amount of money that people spend at Don Mcalds fast
food place is $7.8100 with a standard deviation of $1.5600. 14
customers are randomly selected. Please answer the following
questions, and round all answers to 4 decimal places where possible
and assume a normal distribution.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
What is the probability that one randomly selected customer
will spend less than $7.8847?
For...

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 43
minutes and standard deviation 23 minutes. A researcher observed 11
students who entered the library to study. Round all answers to 4
decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student...

2. A survey was taken place on which fast food restaurant people
like. In a total of 100 participants, 68 people liked McDonalds, 48
people liked Burger King and 21 people like both McDonalds and
Burger King. What is the probability that a randomly selected
participant:
1.) Only likes McDonalds?
2.) Does not like either McDonalds or Burger King?
3.) Likes McDonalds or Burger King phones but not both?
4.) Likes both McDonalds and Burger King phones?

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 46
minutes and standard deviation 19 minutes. A researcher observed 9
students who entered the library to study. Round all answers to 4
decimal places where possible.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
If one randomly selected student...

Suppose that the amount of time that students spend studying in
the library in one sitting is normally distributed with mean 49
minutes and standard deviation 19 minutes. A researcher observed 14
students who entered the library to study. Round all answers to 4
decimal places where possible. What is the distribution of X X ? X
X ~ N(,) What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) What is
the distribution of ∑...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 34 minutes ago

asked 34 minutes ago

asked 46 minutes ago

asked 51 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago