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Assume that random guesses are made for nine multiple choice questions on an SAT test, so that there are n=9 trials, each with probability of success (correct) given by p=0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
Access and download the Charity dataset at https://www.kaggle.com/katyjqian/charity-navigator-scores-expenses-dataset
Load the data into R (or Python, etc)
(a) Plot a histogram of “Funding Efficiency in $ (amount spent to raise $1 in donations)” – it’s the variable fund_eff
(b) Is this a continuous or discrete random variable?
(c) What is the theoretical range of this random variable? What is its observed range?
(d) What are its mean and standard deviation?
(e) Present 5 different histogram versions (vary the bin size, number of bins)
(f) Comment on the shapes of these histograms. Do they tell a similar shape story?
(g) Present one histogram (your favorite of the bunch) with a smooth (kernel) density superimposed to do that in R, you can use the command lines( density(fund_eff) )
(h) Among all the densities and pmfs we’ve learned about, pick one that you think most closely resembles the shape of the histogram.
The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean and standard deviation for the players height. height (in) 70-71 72-73 74-75 76-77 78-79 80-81 82-83 frequency 1 8 13 8 15 6 3
a .Coke b.fanta c.neither Coke or fanta
d.either Coke or fanta
A credit union bank needs to forecast monthly loan requests. Assume the time series is stationary. Answer questions 2-1, 2-2, and 2-3.
2-3 Two months later, at the end of t=24, there is one month left before the end of the quarter. The most recent records collected are now available as Y23=3.895, and Y24 = 4.2. Should management expect some funds left unused at the end of the quarter, if the amount made available to meet loan requests were 12.5 million at the beginning of the quarter? Use the same weighted moving average (of 0.7, and 0.3)
a. Yes. Amount left = 12.5 - 3.895 - 4.2 - 4.12
b. Yes. Amount left = 12.5 - 3*4.12
c. Impossible to answer. Y25 is unknown.
d. Calculate F(25) = F(24+1), then the amount left =12.5 - 3*F(25).
e. None of the above
Suppose that a random variable X has a DISCRETE distribution with probability mass function given as: P(x) = ( x / 2485 if x = 1, 2, . . . , 70 0 Otherwise a) Find P(x > 5) b) Find P(2 ≤ x ≤ 68) c) Find P(x = 70.5)
A random sample of 64 bags of white cheddar popcorn weighed, on avarage, 5.23 ounces with a standard deviation of 0.24 ounces. Test the hypothesis that mean = 5.5 ounces against the alternative hypothesis, mean < 5.5 ounces at the 0.05 level of significance.
in the mmttg, for each of a random sample of 10 men, aged between 35 years and 40 years,
from a particular population.
X 13 23 29 35 17 34 25 20 31 27
Y 103 115 124 126 108 120 113 117 118 119
a) Calculate the coefficient of correlation of the distribution. Interpret your results.
b) Compute the coefficient of determination and interpret your results.
c) Find the Simple regression line of Y on X.
d) Use your equation to estimate the SBP of a man from this population who is aged
38 years and who has a BMI of 30.
at least one smart phone. If a small sample of 40 people is selected from the population
for a statistical investigation, Use the Binomial distribution to estimate the probability that,
the number of people in the sample that have at least one smart phone is;
a) at most 15;
b) more than 12 but fewer than 18;
c) exactly equal to the mean of the distribution
#331389 on Nov 2022