# Tutor profile: Crystal H.

## Questions

### Subject: Basic Math

You have a farm with 15 goats and 20 chickens. a. What is the ratio of goats to chickens? b. What is the percentage of goats on the farm?

a. ratio of goats to chickens is 15:20 or 3:4 in simplest form. b. Percentage of goats on the farm is 15/35 or 42.8%

### Subject: Statistics

A family wishes to have 3 children. Let X be the number of girls. Find the probability distribution of X and expected value.

X can take on the values 0,1,2,3 so I need to find the probabilities of each. There are two methods. Method 1: Since the probability of having a boy or girl is the same, the sample space and count the number of outcomes in each case for X and divide by the total number of outcomes in the sample space. S = {ggg, ggb, gbg, bgg, bbg, bgb, gbb, bbb}. So the probability distribution function is: p(0) = 1/8; p(1) = 3/8; p(2) = 3/8; p(3) = 1/8 .(Note it is good to check that this adds up to 1). Method 2: binomial random variable. A “success” is having a girl. There are n=3 trials, p=0.5 each time and the trials are independent. Hence we can use the formula for the probability distribution function for binomial: p(x) = nCx(0.5)^x(0.5)^(n-x) The expected value is np = 3*.5 = 1.5 So, the expected number of girls is 1.5 girls out of 3.

### Subject: Algebra

You are working at the local pool as a concession stand attendant. You are selling nachos and bottled drinks. Nachos costs $1.50 and drinks costs $.50. At the end of the day, you sold a total of $52 and 50 items. You need to tell your supervisor how many nachos and drinks you sold. What total amounts should you tell your supervisor?

x = amount of nachos y = amount of drinks Amount of items sold equation: x + y = 50 Amount of money sold equation: $1.50x + $.50y = $52 This can be solved by graphing, substitution, or elimination. Solve by graphing and show that the point of intersection is (27, 23) This means that 27 nachos and 23 drinks were sold at the local pool that day.

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