The average amount of money that people spend at Don Mcalds fast food place is $7.3500 with a standard deviation of $1.9700. 8 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 a? - N( c. What is the distribution of a? a- N d. What is the probability that one randomly selected customer will spend more than $6.7253? e. For the 8 customers, find the probability that their average spent is more than $6.7253. f. Find the probability that the randomly selected 8 customers will spend more than $53.8024. g. For part e) and f), is the assumption of normal necessary? ONo Yes h. The owner of Don Mcalds gives a coupon for a free sundae to the 4% of all groups of 8 people who spend the most money. At least how much must a group of 8 spend in total to get the free sundae? $
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![The average amount of money that people spend at Don Mcalds fast food place is $7.3500 with a standard
deviation of $1.9700. 8 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 a? a- N(
c. What is the distribution of x? x
d. What is the probability that one randomly selected customer will spend more than $6.7253?
e. For the 8 customers, find the probability that their average spent is more than $6.7253.
f. Find the probability that the randomly selected 8 customers will spend more than $53.8024.
g. For part e) and f), is the assumption of normal necessary? O No Yes
h. The owner of Don Mcalds gives a coupon for a free sundae to the 4% of all groups of 8 people who spend
the most money. At least how much must a group of 8 spend in total to get the free sundae? $
Hint:
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Hint](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d201130-f4f7-4c89-8a7d-8eb0f7158013%2F9a13417d-0ddb-4462-ba0f-b5664adbd833%2F5w385ur_processed.jpeg&w=3840&q=75)
Given:
The average amount of money spent at Don Mcalds fast food place is $7.3500 and standard deviation is $1.9700. The number of randomly selected customers is 8.
(a)
To find the distribution of X as follows,
Therefore, the distribution of X is as follows,
(b)
To find the distribution of as follows,
Therefore, the distribution of is as follows,
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