Question

For each of the following questions, use Microsoft Excel to find the solution. Be sure to describe which functions you used and how you got the answer. Feel free to use whatever approach you want to get the right answer. Here are some functions you might find useful:
BINOM.DIST

POISSON.DIST

HYPGEOM.DIST

NORM.DIST

Over the next 30 days, the pool has a 15% chance of closing each day. The closings are independent from each other. What is the probability that the pool closes for 11 days? What is the probability that the pool closes 8 days or less?

In a 20 day period, a car wash had 600 customers. Assuming that the car wash is open 24/7, what is the probability that the car wash gets 20 customers on a given day? What is the probability that the car wash gets less than 20 customers on a given day? What about the probability of more than 20?

If there are 70 blue marbles and 45 red marbles in a bowl and I draw 30 of them, what is the probability that I will draw exactly 20 blue marbles? What is the probability that I draw more than 20?

What does the function NORM.DIST do? When hypothesis testing, why should we put 1 in the cumulative option rather than 0? How is NORM.S.DIST different? What about NORM.INV?

For a normal distribution with µ = 24 and σ = 5. What is the probability of getting a result of less than 27? What about a result of more than 20? What is the 60^thpercentile? Find a 95% confidence interval.

Suppose you want to know whether ECON 202 students are the same age as ECON 201 students. Your ECON 201 sample has the following ages: 20, 19, 21, 21, 18, 19. Your ECON 202 sample has the following ages: 21, 20, 21, 20, 21, 22. Under data analysis conduct a t-test or use T.TEST to find the p-value. Assume that the variances are different (option 3). At what level can you reject the null hypothesis?

Answer 1

Let X is a random variable shows the number of days pool close. Here X has binomial distribution n=30 and p=0.15.

The probability that the pool closes for 11 days is:

The excel function used is: "=BINOMDIST(11,30,0.15,FALSE)"

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The probability that the pool closes 8 days or less is

The excel function used is: "=BINOMDIST(8,30,0.15,TRUE)"

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Average number of customers per day is

Let X is a random variable shows the number of customers per day. Here X has Poisson distribution with parameter .

The probability that the car wash gets 20 customers on a given day is

Excel function used: "=POISSON(20,30,FALSE)"

The probability that the car wash gets less than 20 customers on a given day is

Excel function used: "=POISSON(19,30,True)"

The probability that the car wash gets more than 20 customers on a given day is

Excel function used: "=1-POISSON(20,30,True)"