Probablility

The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 7 ounces. 32 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected person drinks between 16.6 and 17.2 ounces of coffee per day?
4. For the 32 people, find the probability that the average coffee consumption is between 16.6 and 17.2 ounces of coffee per day.
5. For part d), is the assumption that the distribution is normal necessary? YesNo
6. Find the IQR for the average of 32 coffee drinkers.
   Q1 =  ounces
   Q3 =  ounces
   IQR:  ounces

2.

The amount of syrup that people put on their pancakes is normally distributed with mean 65 mL and standard deviation 7 mL. Suppose that 9 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. If a single randomly selected individual is observed, find the probability that this person consumes is between 65.8 mL and 67.9 mL.
4. For the group of 9 pancake eaters, find the probability that the average amount of syrup is between 65.8 mL and 67.9 mL.
5. For part d), is the assumption that the distribution is normal necessary? NoYes

3.

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 110 and a standard deviation of about 55. Assume forty-nine individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 49, find the probability that the average number of friends is more than 109.
3. Find the third quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? YesNo

4.

The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.7 ppm and standard deviation 1.3 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected city’s waterway will have less than 10 ppm pollutants?
4. For the 38 cities, find the probability that the average amount of pollutants is less than 10 ppm.
5. For part d), is the assumption that the distribution is normal necessary? NoYes
6. Find the IQR for the average of 38 cities.
   Q1 =  ppm
   Q3 =  ppm
   IQR:  ppm

5.

The average score for games played in the NFL is 21.3 and the standard deviation is 9.1 points. 17 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
3. P(¯xx¯ < 23.0894) =
4. Find the 69th percentile for the mean score for this sample size.
5. P(18.1894 < ¯xx¯ < 23.3036) =
6. Q1 for the ¯xx¯ distribution =
7. P(∑x∑x > 358.5198) =
8. For part c) and e), is the assumption of normal necessary? YesNo

6.

The average amount of money that people spend at Don Mcalds fast food place is $7.5400 with a standard deviation of $1.8500. 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.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. What is the probability that one randomly selected customer will spend less than $7.8333?
5. For the 11 customers, find the probability that their average spent is more than $7.8333.
6. Find the probability that the randomly selected 11 customers will spend more than $86.1663.
7. For part e) and f), is the assumption of normal necessary? NoYes
8. The owner of Don Mcalds gives a coupon for a free sundae to the 3% 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? $

7.

A computer selects a number XX from 0 to 5 randomly and uniformly. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ U(,)
2. Suppose that the computer randomly picks 37 such numbers.  What is the distribution of ¯xx¯ for this selection of numbers. ¯xx¯ ~ N(,)
3. What is the probability that the average of 37 numbers will be more than 2.8?