Answer:
2/15
Step-by-step explanation:
Given that :
pretzel = 4
Popcorn = 3
Cheddar cracker = 3
Total = 4 + 3 + 3 = 10
Probability = Required outcome / Total possible outcomes
Selecting with replacement :
First selection :
P(pretzel bag) = 4 / 10
Second selection :
P(pretzel bag) = 3 / 9
P(2 pretzel bags) = 4/10 * 3/9 = 12 / 90 = 2/15
Answer: $408.96
Step-by-step explanation:
Part a)
The simple random sample of size n=36 is obtained from a population with

and

The sampling distribution of the sample means has a mean that is equal to mean of the population the sample has been drawn from.
Therefore the sampling distribution has a mean of

The standard error of the means becomes the standard deviation of the sampling distribution.

Part b) We want to find

We need to convert to z-score.

Part c)
We want to find

We convert to z-score and use the normal distribution table to find the corresponding area.

Part d)
We want to find :

We convert to z-scores and again use the standard normal distribution table.

Separate the variables:

Separate the left side into partial fractions. We want coefficients a and b such that





So we have

Integrating both sides yields






With the initial condition y(0) = 1, we find

so that the particular solution is

It's not too hard to solve explicitly for y; notice that

Then





