The “Love Our Earth” organization has promoted “Bring Your Own Cup” for years. A recent survey conducted by “Love Our Earth” and a café revealed that 17% of the customers bring their own cups for take away order when purchasing iced coffee. The selling price of an iced coffee is $28 while customers can get a $2 discount when they bring their own cups. There are 15 customers in the line waiting for the take away order of iced coffee. (a) What is the probability that exactly 3 customers bring their own cups? (b) What is the probability that there are at least 3 customers bring their own cups? (c) Most likely, how many customers in the line would have brought their own cups? What is the probability of its happening?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Question 1
The “Love Our Earth” organization has promoted “Bring Your Own Cup” for years. A recent survey
conducted by “Love Our Earth” and a café revealed that 17% of the customers bring their own cups for take
away order when purchasing iced coffee. The selling price of an iced coffee is $28 while customers can get
a $2 discount when they bring their own cups. There are 15 customers in the line waiting for the take away
order of iced coffee.
(a) What is the probability that exactly 3 customers bring their own cups?
(b) What is the probability that there are at least 3 customers bring their own cups?
(c) Most likely, how many customers in the line would have brought their own cups? What is the
probability of its happening?
(d) Calculate the expectation, variance, and standard deviation of the income by selling 15 cups of iced coffee.
Question 2
Alex is running a recycling business. The weight of collected used Iron in a day is a variable, X, which is
Iron is $15 and the other cost for running the recycling business per day is $2300, the total expense per day,
T, is given by T = 15X + 2300.
(a) Find mean and the standard deviation of T.
(b) There is a 13.8% chance that the total daily expense of the business is more than $K. Find the value of
K.
(c) Suppose each kg of collected used Iron can be sold for $35 after the recycling. Find the mean, median
and the standard deviation of the daily profit of the business.
(d) Alex can apply for government allowance if there is more than 10% chance that his recycling business
has negative profit in a day. Can he apply for the government allowance? Explain your answer with
calculation.
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