Suppose that the weight of pears from California is normally distributed with a mean of 9 ounces and a standard deviation of 1.5 ounces.

a. What is the probability of selecting a pear that weighs more than 12 ounces?

b. What is the probability of selecting a pear that weighs less than 6 ounces?

c. What is the probability of selecting a pear that weigh exactly 10.5 ounces?

d. What is the probability of selecting a pear that weighs between 7.5 and 10.5 ounces?

preform a Monte Carlo simulation in R to generate the probability distribution of the sum of two die (for example 1st die is 2 and second die is 3 the random variable is 2+3=5). The R-script should print out (display in R-studio) or have saved files for the following well labeled results:

1. Histrogram or barchart of probability distribution

2. Mean of probability distribution

3. Standard deviation of probability distribution

Suppose we know that a random variable X has a population mean µ = 400 with a standard deviation σ = 100. What are the following probabilities? (12 points)

The probability that the sample mean is above 376 when n = 1600.

The probability that the sample mean is above 376 when n = 400.

The probability that the sample mean is above 376 when n = 100.

The probability that the sample mean is above 376 when n = 64.

The weight of trout in a fish farm follows the distribution N(200,502). A trout is randomly selected. (a) What is the probability that its weight does not exceed 175g? (b) What is the probability that its weight is greater than 230g? (c) What is the probability that its weight is between 225g and 275g? (d) What is the probability that out of eight trout selected randomly from the fish farm, less than three of them will not weigh more than 175g?

The probability of selecting a company that has a return on assets above 15 percent is 32 percent. The probability of selecting a company that has a dividend payout ratio at or above 40 percent is 39 percent. The probability of selecting a company with a return on assets above 15 percent and a dividend payout at or above 40 percent is 7 percent. What is the probability of selecting a company that has a return on assets of 15 percent or a dividend payout at or above 40 percent? _______ (

0. Foot length (in inches) of a randomly chosen adult male is a normal random variable with a mean of 11 and standard deviation of 1.5. Use this information and the z-table to answer the following questions a-j.

   1. On average, what is a randomly chosen adult male’s foot length?

   2. Let X denote the foot length of a randomly chosen adult male. What is the distribution of X?

   3. What is the probability that a randomly chosen adult male’s foot length will be less than 10?

   4. What is the probability that a randomly chosen adult male’s foot length will be less than 14?

   5. What is the probability that a randomly chosen adult male’s foot length will be between 10 and 13?

   6. What is the probability that a randomly chosen adult male’s foot length will be between 11 and 14?

   7. What is the probability that a randomly chosen adult male’s foot length is greater than 12?

   8. What is the probability that a randomly chosen adult male’s foot length is greater than 13?

   9. Find the foot length “c” such that probability of a randomly chosen adult male’s foot length greater than c is 0.5.

   10. Find the foot length “r” such that probability of a randomly chosen adult male’s foot length less than r is 0.2.

A card is drawn at random from a deck of 52 cards. Find the probability that the card is a seven or a spade.

A bag contains 7 green marbles, 5 blue marbles, and 3 yellow marbles. If a marble is randomly picked from the bag, find the probability that it is not blue.

Ten balls labeled with the numbers 1, 2, ..., 10 are in a bin. What is the probability that the numbers 8, 7, and 2 are drawn in that order from the bin if the ball selected is not returned to the bin before the next ball is selected.

What is the probability that Joseph, Anne, and Sue win the first, second, and third prizes, respectively, in a drawing if 20 people enter the contest and winning more than one prize is allowed?

Two cards are drawn at random from a deck of 52 cards without replacement. What is the probability that both cards are clubs?

Two cards are drawn at random from a deck of 52 cards with replacement. What is the probability that both cards are clubs?

What is the probability that a positive integer not exceeding 100 selected at random is divisible by 3 or 5?

A committee of 5 people is to be selected from a group of 10 people consisting of 3 men and 7 women. What is the probability that 2 men and 3 women are on the committee?

1. The total weight of vehicles on a parking deck is uniformly distributed on the interval [200, 300] (thousands of pounds). Find the probability that the total vehicle weight is:
   1. Less than 250 thousand pounds.
   2. Between 225 and 275 thousand pounds.
   3. Between 275 and 325 thousand pounds.
   4. At least 250 thousand pounds.
2. Vehicles arrive at a car wash at an exponential rate of 7 per hour.
   1. Find the probability that the time between arrivals is between 10 and 30 minutes
   2. Find the probability that at least 15 minutes elapses without an arrival.
   3. Find the time t where there is a 50% chance that the next customer arrives within t minutes of the last.
3. The attendance at a college athletic event can be approximated with a normal distribution that has a mean of 10,000 and a standard deviation of 2300.
   1. Find the probability that an athletic event’s attendance is less than 12,000.
   2. Find the probability that an athletic event’s attendance is less than 5000.
   3. Find the probability that an athletic event’s attendance is between 12,000 and 14,000.
   4. Find the probability that an athletic event’s attendance is at least 7700.
   5. Find the probability that an athletic event’s attendance is between 8000 and 11,000.
   6. 20% of games have an attendance below what level?
   7. 10% of games have an attendance above what level?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the expected number of customers that will take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that at least three take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that exactly three take the discount (round answers to three decimal places, for example, 0.xxx)?

A firm gives discounts to its customers who pay their bills on time. A customer receives a ten percent discount on the next invoice when a bill is paid in full before its due date. Thirty percent of all customers use the discount. If the company sends out eight bills, what is the probability that less than three take the discount (round answers to three decimal places, for example, 0.xxx)?

Python code

def overlap(user1, user2, interests):
""" Return the number of interests that user1 and user2
have in common """
return 0

  
def most_similar(user, interests):
""" Determine the name of user who is most similar
to the input user defined by having the most interests
in common. Return a tuple: (most_similar_user, num_interests_in_common) """
return ("", 0)
  

def recommendations(user, interests):
""" Find the user who shares the most interests with the specified user.
Recommend to user any interests that his or her closest match has
that are not already in the user's list of interests.
Return a list of recommendations. """
return []

#%% Don't change this:
  
interests = {
"Pam":["Hadoop", "Big Data", "HBase", "Java", "Spark", "Storm", "Cassandra"],
"Ann":["NoSQL", "MongoDB", "Cassandra", "HBase", "Postgres"],
"Raj":["Python", "scikit-learn", "scipy", "numpy", "statsmodels", "pandas"],
"Jim":["R", "Python", "statistics", "regression", "probability", "programming languages"],
"Eve":["machine learning", "regression", "decision trees", "libsvm"],
"Carl Yastrzemski":["Python", "R", "Java", "C++", "Haskell", "programming languages"],
"Sam":["statistics", "probability", "mathematics", "theory"],
"Una":["machine learning", "scikit-learn", "Mahout", "neural networks"],
"Liv":["neural networks", "deep learning", "Big Data", "artificial intelligence"],
"Bob":["Hadoop", "Java", "MapReduce", "Big Data"],
"Jon":["statistics", "R", "statsmodels"],
"Tom":["pandas", "R", "Python"],
"Tim":["databases", "HBase", "Postgres", "MySQL", "MongoDB"],
"Hal":["libsvm", "regression", "support vector machines"],
"Joe":["C++", "deep learning", "artificial intelligence", "probability"]
}

#%% Don't change this either!

for user in interests.keys():
print(user, recommendations(user, interests))

#%% Put output here

"""
Your output
"""