I have a few questions on my homework assignment. I've been sick and I have no idea what I'm doing.

Question 1: Assume the hights of high school bball players are normally distributed. For the boys the mean is 74" with a standard deviation of 4.5" while girl players have a mean height of 70" and a standard deviation of 3". At a mixed 2 on 2 tournament teams are formed by randomaly pairing boys with girls as teammates.
a. On average how much taller do you expect the boy to be
b. What will be the standard deviation of the difference in teammates heights
c. On what fraction of the teams would you expect the girl to be taller than the boy
Question 2: 62% of all purchases are made by credit cards on a typical day you make 20 sales
a. What is the probablity that your 4th customer is the first one who uses a credit card
b. Let X represent the number of coustomers who use a credit card on a typical day. What is the probablity model for X Specify the model (name and parameters), and tell the mean and standard deviation.
c. What is the probability that on a typical day at least 1/2 your customers use a credit card?

Sure, I can help you with your homework assignment. Let's break down each question and discuss how to find the answers.

Question 1:
a. On average, how much taller do you expect the boy to be?
To find the average height difference between boys and girls, subtract the mean height of girls from the mean height of boys.
Average Height Difference = Mean Boy's Height - Mean Girl's Height = 74" - 70" = 4"

b. What will be the standard deviation of the difference in teammates' heights?
To find the standard deviation of the difference in teammates' heights, you need to consider the variability of both the boy and girl heights. The standard deviation of the difference can be calculated using the formula:
Standard Deviation of Difference = √(Standard Deviation Boy^2 + Standard Deviation Girl^2)
Standard Deviation Boy = 4.5"
Standard Deviation Girl = 3"
Standard Deviation of Difference = √(4.5"^2 + 3"^2) = √(20.25 + 9) = √29.25 ≈ 5.41"

c. On what fraction of the teams would you expect the girl to be taller than the boy?
To find the fraction of teams where the girl is taller than the boy, you need to find the probability that a randomly chosen girl's height is greater than the height of a randomly chosen boy. Since the heights of boys and girls are normally distributed, you can use the z-score to calculate this probability.
The z-score can be calculated using the formula:
z = (x - mean) / standard deviation
where x is the height, mean is the mean height, and standard deviation is the standard deviation of the respective group.
Then, you can use a standard normal distribution table or a z-score calculator to find the corresponding probability. The resulting probability will give you the fraction of teams where the girl is taller than the boy.

Question 2:
a. What is the probability that your 4th customer is the first one who uses a credit card?
Assuming each customer's behavior (using a credit card or not) is independent, you can calculate the probability as follows:
Probability = (Probability of using a credit card) * (Probability of not using a credit card) * (Probability of not using a credit card)
Probability = (0.62) * (0.38) * (0.38) [since 62% use a credit card, 100% - 62% = 38% don't use a credit card]
Probability = 0.1449 or 14.49%

b. Let X represent the number of customers who use a credit card on a typical day. What is the probability model for X? Specify the model (name and parameters), and tell the mean and standard deviation.
In this scenario, the number of customers who use a credit card follows a binomial distribution, as customers either use a credit card (success) or not (failure) with a known probability of success (0.62 in this case). The binomial distribution has two parameters: n (number of trials) and p (probability of success).
In this case, the parameters are:
n = 20 (as there are 20 sales in a typical day)
p = 0.62 (probability of using a credit card)

The mean (μ) of the binomial distribution is given by:
μ = n * p = 20 * 0.62 = 12.4

The standard deviation (σ) of the binomial distribution is given by:
σ = √(n * p * (1 - p)) = √(20 * 0.62 * 0.38) ≈ 2.23

c. What is the probability that on a typical day at least 1/2 your customers use a credit card?
To calculate this probability, we can find the cumulative probability of having less than half the customers using a credit card and subtract it from 1.
Probability = 1 - P(X < 0.5n) = 1 - P(X ≤ 10) [since n = 20]
Here, P(X ≤ x) denotes the cumulative probability of having up to x customers using a credit card, which can be calculated using the binomial distribution formula or a binomial probability calculator.