Statistics and Probability Answers

Student population of a university has 30% asian, 40% american, 20% european and 10% african students. It is known that 40% of all asian students, 50% of all american students, 60% of all european students and 20% of all african students are girls. Find the probability that a girl chosen at random from the university is an asian?

In a normal distribution 31% of the items are under 45 and 8% are over 64. Find the mean and standard deviation of the distribution

The following table give the numbers of orders received for a sample of 30 hours at the Timesaver Mail Order Company.
34 44 31 52 41 47 38 35 32 39 28 24 46 41 49 53 57 33 27 37 30 27 45 38 34 46 36 30 47 50

Construct a frequency distribution table, calculate cumulative frequency for all classes and draw an ogive for the above distribution.

Explain in your own words the statement at the bottom of page 63: "the probability that X is exactly 0.5 (or exactly anything) is precisely 0." Make sure your explanation reconciles the following:
Doesn't the pointer need to land somewhere?
Have you used the words "discrete" or "continuous" in your answer? Have you referred back to the definition of the word "continuous"?
Make sure you use the notion of infinite precision. Don't confuse precision with accuracy. Precision is a number of decimal places.
How would this scenario change if there were pegs on the edge of the circle, like the Wheel-of-Fortune wheel shown below?

How will yoi use the sturge's appriximation to draw a frequency distribution table?

How will you draw a tree diagram on probability?

How will yoi use the sturge's appriximation to draw a frequency distribution table?

Following data of performance scores is available of employees working with a company. You are required to perform the following: a. Make the frequency distribution, Calculate the frequency and the Cumulative frequency b. Calculate the mean, median, quartiles and Mode c. Calculate the variance and the standard deviation Table: Performance score of the employees: TABLE BELOW 52 33 70 95 57 61 47 60 57 64 54 94 38 61 89 48 50 39 94 63 59 31 88 46 68 88 93 48 82 82 72 73 74 70 92 76 98 91 80 68 32 33 31 75 54 48 62 53 36 64 63 66 92 98 91 42 36 54 71 86 84 55 33 43 91 34 64 67 89 78 47 62 97 92 53 56 68 55 36 67 93 42 51 77 36 93 51 66 44 66 63 33 68 79 92 76 83 53 86 76 35 40 43 46 55 41 36 39 42 96 42 77 60 53 38 51 95 56 93 63 48 69 49 33 95 37 83 64 83 62 96 34 85 32 40 85 39 59 77 62 35 34 39 92 54 89 36 45 83 34 86 90 39 61 88 86 55 33 77 40 69 54 30 38 79 77 44 59 95 34 38 91 80 90 58 40 88 45 95 71 80 43 89 53 61 40 31 61 58 53 88 94 91 63 60 94 98 53 53 45 50 34 75 74 90 98 87 66

2. Suppose a researcher wanted to estimate people’s willingness to pay for public construction project. He
asked to i-th respondent that “Are you willing to pay Ai amount of tax for public construction project?”, and
the respondent would only say yes or no. Suppose people’s willingness to pay follows normal distribution
with mean μ and variance σ2 , derive likelihood function to estimate mean μ and variance σ2 based on the
responses(yes or no) of n respondents. (Hint: A respondent will accept an offer if his/her willingness to pay
is larger than the given amount of tax A) (20 points)

1. Airline companies usually sell tickets more than the number of seats they have because a certain number of
ticketed passengers will cancel at the last minute. Suppose an airplane has 300 seats, no-show rate is 7%, and
there is no penalty for cancellation. When ticket price is $1,000, and overbooked flight compensation is $1,500
per passenger, what is the optimal overbooking ratio to maximize profit? Use R program and attach the R
code with results. (30 points)