Basic Statistics and Probability

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? ____________________________