2) The amount of beer (on tap) that a bar sells in a day follows a Normal distribution with a mean of 15 gallons and a standard deviation of 2 gallons.

1. What is the probability that the bar sells more than 16.15 gallons of beer on a day?

2. What is the probability that the bar sells more than 1525 gallons of beer over one hundred days?

3. What is the probability (or your best approximation of this probability) that the average amount the bar sells over 15 days is less than 14.7 gallons? Do you need to use a t distribution to answer this question?

4. The bar owner is concerned whenever less than 12.5 gallons of beer are sold in a day – refer to such a day as a “Bad Demand Day.” What is the probability that over the next 100 days, the bar has more than 14 “Bad Demand Days”?

A deck consists of cards with 5 suits labelled A to E and numbered ranks from 1 to 6

. Each card is equally likely to be drawn.

Suits A

to C

are red.

Suits D

to E

are blue.

A card is drawn at random from this deck.

1) What is the probability of it having a rank less than or equal to 2 given it has a rank less than or equal to 3?

2)What is the probability that the second card is blue?

3)What is the probability that the second card is blue given that the first card is red?

4)What is the probability that the second card is blue given that the first card is blue?

5)What is the probability that the second card is blue given that the first card has rank 1?

Hint: try cases based on the color of the first card.

In a certain college, 33% of all physics students belong to the math club. Explain the method used and calculate the following:

a. Does this scenario meet the criteria of a bimodial probability distribution? Justify your answer by verifying each of the four conditions.

b. If 10 students are selected at random from the physics majors, what is the probability that exactly 6 belong to the math club?

c. If 10 students are selected at random from the physics majors, what is the probability that less than 6 belong to the math club

d. What is the probability that no more than 6 belong to the math club?

e. What is the probability that more than 6 belong to the math club?

f. Address the importance of understanding the terms "less than", "no more than", "greater than"

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3306 grams and a standard deviation of 586 grams.

What is the probability that a randomly selected baby weighs between 3200 grams and 3700 grams? Round your answer to 4 decimal places.

What is the probability that the average weight of 21 randomly selected babies is between 3200 grams and 3700 grams? Round your answer to 4 decimal places.

Why did the probability increase?

A)The probability increased since the sample size increased and the distribution of sample means is more spread out.

B)The probability increased since the sample size increased and the sample means are more concentrated near the mean of 3306.

. A sample of 500 respondents was selected in a large metropolitan area to study consumer behavior, with the following results shown through the contingency table:

In the EAI sampling problem, the population mean is $51,800 and the population standard deviation is $4,000. When the sample size is n = 20, there is a 0.4238 probability of obtaining a sample mean within +/- $500 of the population mean. Use z-table.

1. What is the probability that the sample mean is within $500 of the population mean if a sample of size 40 is used (to 4 decimals)?
   
   
2. What is the probability that the sample mean is within $500 of the population mean if a sample of size 80 is used (to 4 decimals)?

A population proportion is 0.4. A sample of size 300 will be taken and the sample proportion  will be used to estimate the population proportion. Use z-table.

Round your answers to four decimal places.

a. What is the probability that the sample proportion will be within ±0.02 of the population proportion?

b. What is the probability that the sample proportion will be within ±0.08 of the population proportion?

2. A child has a collection of 28 dyed eggs. There are 10 pink eggs, 8 green eggs, 6 yellow eggs, and 4 blue eggs. Suppose the child selects 6 eggs at random without replacement from this collection.

a) Find the probability the 6 eggs contain exactly 3 pink eggs.

b) Find the probability the 6 eggs contain 2 pink eggs, 1 green egg, 2 yellow eggs, and 1 blue egg.

c) Find the probability the 6 eggs contain exactly 2 green eggs and exactly 2 blue eggs.

d) Find the probability that half of the 6 eggs are pink and the other half are green.

e) Find the probability that none of the 6 eggs are pink and none of the 6 eggs are green.

Watch your cholesterol: The mean serum cholesterol level for U.S. adults was 204, with a standard deviation of 42.5
(the units are milligrams per deciliter). A simple random sample of 112 adults is chosen. Use the TI-84 calculator.
Round the answers to four decimal places.

Part 1 of 3
What is the probability that the sample mean cholesterol level is greater than 212?
The probability that the sample mean cholesterol level is greater than 212 is?

Part 2 of 3
What is the probability that the sample mean cholesterol level is between 192 and 202?
The probability that the sample mean cholesterol level is between 192 and 202 is?

Part 3 of 3
Would it be unusual for the sample mean to be less than 197?
It (would/wouldnt) be unusual for the sample mean to be less than 197, since the probability is?

A. Bree and Kendra love to go to the movies. When they go, there is a probability of 0.3 that Bree will buy popcorn. The probability that Kendra will buy popcorn is 0.35 if Bree buys popcorn and 0.65 if Bree does not. When Bree and Kendra go to the movies together, find the probability that

1. both buy popcorn;
2. neither buys popcorn;
3. exactly one of them buys popcorn;

B. Carmelita accompanies Bree and Kendra to the movies sometimes. During these trips, the probability that Carmelita buys popcorn is 0.55 if both Bree and Kendra buy popcorn and 0.4 if exactly one of Bree and Kendra buys popcorn. When Bree, Kendra, and Carmelita go to the movies together, find the probability that

4. all three buy popcorn;

5. Kendra and Carmelita buy popcorn, but Bree does not;