37​% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Construct a binomial distribution using n=6 and p=0.37

To construct a binomial distribution, we need to calculate the probabilities of each possible outcome (0 to 6) for the random variable, which represents the number of working mothers (out of 6) who do not have enough money to cover their health insurance deductibles. 

The parameters are:
- \( n = 6 \) (the number of trials, or working mothers selected),
- \( p = 0.37 \) (the probability that a working mother does **not** have enough money to cover deductibles),
- \( q = 1 - p = 0.63 \) (the probability that a working mother **does** have enough money).

The probability mass function (PMF) for a binomial distribution is given by:

\[
P(X = k) = \binom{n}{k} p^k q^{n-k}
\]

Where:
- \( X \) is the random variable representing the number of successes (working mothers who do not have enough money),
- \( k \) is the number of successes (ranging from 0 to 6),
- \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \).

We will now calculate the probabilities for \( k = 0, 1, 2, 3, 4, 5, 6 \).

Let's compute these probabilities.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can still guide you through the manual process of calculating the binomial distribution. Let me know if you'd like that or if you have any other questions!

Here are some relative questions for you to consider:
1. How is the binomial coefficient \(\binom{n}{k}\) calculated?
2. What is the general formula for a binomial distribution?
3. How does the probability \(p\) affect the shape of the distribution?
4. What are the mean and variance formulas for a binomial distribution?
5. How can you use binomial distribution to calculate cumulative probabilities?

**Tip**: In binomial distributions, the sum of all individual probabilities must always equal 1.

37​% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Construct a binomial distribution using n=6 and p=0.37.

Explore the solution to a probability problem involving binomial distribution. Calculate the probabilities of various outcomes where 37% of working mothers do not have enough money to cover their health insurance deductibles. This step-by-step guide includes key formulas and the binomial theorem.

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