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Basic Statistics and Probability

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Dear OTA,

Help me with the attached problems with steps.

Thanks

1. Linda owns a small business. Use the probability distribution below, where X represents the number of employees who call in sick on a given day. (2 points each)

Number of Employees Sick 0 1 2 3 4
P(X = x) 0.05 0.45 0.15 0.1

a. P(X = 2) is ______________________
b. The expected value (Mean) of the number of employees calling in sick on any given day is ____________________
c. The standard deviation for the random variable X is __________________

2. According to the Information Please Almanac, 6% of the human population is blood type O-negative. A simple random sample of size 4 is obtained, and the number of people X with blood type O-negative is recorded. (Binomial) 2 points each

a. The probability that exactly 3 out of 4 have blood type O-negative is ____________
b. The expected value (Mean) is ____________________
c. The standard deviation is ___________________

3. The number of chocolate chips in an 18-ounce bag of Chips Ahoy! Chocolate chip cookies are approximately normally distributed with a mean of 1262 chips and standard deviation 118 chips. ( 2 points each)

a. The probability that a randomly selected 18-ounce bag of Chips Ahoy! Cookies contains between 1000 and 1400 chocolate chips is ___________________

b. The probability that a randomly selected 18-ounce bag of Chips Ahoy! Cookies contains fewer than 1000 chocolate chips is _____________________

c. The proportion that 18-ounce bags of Chip Ahoy! Cookies contain more than 1400 chocolate chips is _____________________

d. How many chocolate chips does an 18-ounce bag of Chips Ahoy! Chocolate chip cookies need to place in the top 3% of the distribution? _____________________

e. What is the percentile rank of an 18-ounce bag of Chip Ahoy! Cookies that contains 1475 chocolate chips? ____________________________

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This solution gives the step by step method for computing basic statistics and probability.

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Probability Questions

51. The following cross tabulation shows household income by educational level of the Head of household (Statistical Abstract of the United States:2002)

Under 25.0- 50.0- 75.0- 100 or
Education Level 25 49.9 74.9 99.9 more total

Not HS Grads. 9,285 4,093 1,589 541 354 15,862
HS Graduates 10,150 9,821 6,050 2,737 2,028 30, 786
Some college 6,011 8,221 5,813 3,215 3,120 26, 380
Bachelor degree 2,138 3,985 3,952 2,698 4,748 17,521
Beyond Bachelor 813 1,497 1,815 1,589 3,765 9,479
Degree

TOTAL 28,397 27,617 19,219 10,780 14,015 100, 028

A. Develop a joint probability table.
B. What is the probability of a head of household not being a high school graduate?
C. What is the probability of a head of household having a Bachelor's degree or more
Education?
D. What is the probability of a household headed by someone with a Bachelor's degree
Earning $100,000 or more?
E. What is the probability of a household having income below $25,000?
F. What is the probability of a household headed by someone with a Bachelor's degree
Earning less than $25,000
G. Is household income independent of education level?

I need a paragraph that explains mutually exclusive and independent events. In the paragraph answer the questions:
A. What does it mean if two events are mutually exclusive? Give an example
B. What does it mean if two events are dependent? Independent? Give an example
C. Can a pair of events be both mutually exclusive and independent?

See attached file for full problem description.

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