1) Define and elaborate upon the following:
(a) A probability density function
(b) A Poisson distribution
(c) A hypergeometric distribution
(d) What does the value of a probability density function denote?

What is the probability that Z is less than minus − 0.27 0.27 or greater than the​ mean? The probability that Z is less than minus − 0.27 0.27 or greater than the mean is 0.8936

SAT Score Analysis

You have been asked to analyze SAT scores (which may be 400 - 1600).  

You will be analyzing a population (a list) which consists of a number of

samples (lists) of student scores.

Here is the code to generate the  population/samples:

     import random

  population=[]

  for i in range(5):

  sample = []

  n = random.randint(5,10)

  for num in range(n):

  sample.append(random.randrange(400,1600))

  population.append(sample)  

The analysis should be conducted as follows:

  ##calculate the total number of scores  

  ##calculate the total value of all scores

  ##find the average score of the population  

  ##print the total number of scores  

  ##print the total value of all scores

  ##print the average of all of the scores

  ##while a sample has an average that is less than the

  ##average of all scores add a random value 1000 - 1600

  ##to the sample until the average is no longer less than

  ##the average of all scores

  ##please note: this could result in lots of numbers

  ##being appended to the sample

  ##print the population

  ##adjust the population by

  ##removing the highest and lowest scores from each sample

  ##print the (adjusted) population  

  ##calculate the total number of (adjusted) scores  

  ##calculate the total value of all (adjusted) scores

  ##find the average score of the (adjusted) population  

  ##print the total number of (adjusted) scores  

  ##print the total value of all (adjusted) scores

  ##print the average of all of the (adjusted) scores

Sample Output

Python 3.7.2 (v3.7.2:9a3ffc0492, Dec 24 2018, 02:44:43)

[Clang 6.0 (clang-600.0.57)] on darwin

Type "help", "copyright", "credits" or "license()" for more information.

>>>

RESTART: /Users/janetbrownsederberg/Stonehill/Stonehill_Fall_2020/CSC102A_Fall_2020/CSC102_Fall_2020_HomeworkSolutions_JBS/SAT_Analysis_While.py

Population is:

[[1241, 1398, 562, 1247, 1465, 1525, 1328, 825, 1161, 1418], [820, 614, 1299, 1304, 595, 938, 1297], [856, 772, 768, 1396, 625, 559], [975, 883, 1568, 704, 1588, 1485], [1025, 1424, 971, 499, 698, 671]]

Number of scores counted is:

35

Total value of all scores counted is:

36504

Average of all scores is:

1042.9714285714285

Adjusted population is:

[[1241, 1398, 562, 1247, 1465, 1525, 1328, 825, 1161, 1418], [820, 614, 1299, 1304, 595, 938, 1297, 1569], [856, 772, 768, 1396, 625, 559, 1159, 1305, 1152, 1311, 1098, 1336, 1048, 1000, 1547], [975, 883, 1568, 704, 1588, 1485], [1025, 1424, 971, 499, 698, 671, 1511, 1026, 1100, 1510]]

After removal of max an min values the population is:

[[1241, 1398, 1247, 1465, 1328, 825, 1161, 1418], [820, 614, 1299, 1304, 938, 1297], [856, 772, 768, 1396, 625, 1159, 1305, 1152, 1311, 1098, 1336, 1048, 1000], [975, 883, 1568, 1485], [1025, 1424, 971, 698, 671, 1026, 1100, 1510]]

Adjusted number of scores counted is:

39

Adjusted total value of all scores counted is:

43517

Adjusted average of all scores is:

1115.820512820513

>>>

Done in Python Format please. Other codes provided for this question on here were not correct

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15.

What is the probability that a person would score 130 or more on the test?

A..0200

B..0500

C..0228

D..0250

What is the probability that a person would score between 85 and 115?

A..6826

B..6800

C..3413

D..6587

Suppose that you enrolled in a class of 36 students, what is the probability that the class’ average IQ exceeds 130?

A.

almost zero

B.

.0250

C.

.0500

D.

.2280

What is the probability that a person would score between 115 and 130?

"Make a tree diagram to determine the theoretical probability for this experiment: Spin the arrows (not shown) on each of the following three spinners, and note the color where the arrow lands on each spinner. Spinner 1 is divided into two equal sectors, labeled “Red” and “Blue.” Spinner 2 is first divided into two equal sectors. The left is labeled “Green.” The right is then divided into two equal sectors, labeled “Red” and “Blue.” Spinner 3 is divided into three equal sectors, labeled “Red,” “Blue,” and “Green.” Give the sample space for the experiment and the probability of each outcome. What is the probability of getting at least 1 red? What is the probability of getting at least 1 blue?"

There are four urns, which we label A, B, C, and D, and each of these urns contains some white balls and some black balls, as specified below.•UrnAhas3white balls and2black balls•UrnBhas2white balls and6black balls•UrnChas3white balls and6black balls•UrnDhas5white balls and7black balls one of the urns is chosen at random, and then one of the balls is selected from the chosen urn.

(a) What is the probability that urnAis chosen, and then a white ball is chosen from thaturn?

(b) What is the overall probability that a white ball is chosen?

(c) If a white ball is chosen, what is the probability that it came from urnA?

(d) If a black ball is chosen, what is the probability that it came from urnA?

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.

a. Compute the probability of receiving one call in a 5-minute interval of time.

  (to 4 decimals)

b. Compute the probability of receiving exactly 13 calls in 15 minutes.

  (to 4 decimals)

c. Suppose no calls are currently on hold. If the agent takes 10 minutes to complete the current call, how many callers do you expect to be waiting by that time?

What is the probability that none will be waiting?

  (to 4 decimals)

d. If no calls are currently being processed, what is the probability that the agent can take 2 minutes for a personal time without being interrupted by a call?

The daily amount of water drunk by an elephant in Serengeti National Park is evenly distributed between 0 and 60 liters. 1. What is the probability that an elephant drinks only 25 liters of water at during a day? 2. What is the probability that it will take 40 days for an elephant drink at least 45 liters of water for the first time? 3. What is the probability that it will take 11 days for an elephant drink at least 45 liters of water for the fifth time? 4. There is a certain parasite in these elephants. We have identified in average 35 of these parasites per elephant. What is the probability that we find more than 2 parasites on a randomly chosen elephant

10. The following table states how many first, second and third class passengers aboard the Titanic survived (and didn’t). Survived Did not Survive Total First Class 201 123 324 Second Class 118 166 284 Third Class 181 528 709 Total 500 817 1317 (a) What is the probability that a randomly chosen person was in first class? (b) What is the probability that a randomly chosen person was in first class and did not survive? (c) What is the probability that a randomly chosen person was in first class or did not survive? (d) What is the probability that a randomly chosen person was in first class, given that they did not survive?