Let's go through each of the given probability questions step by step:
1. Exactly 15 are employed:
[tex]\[
P(x = 15) \approx 0.0746
\][/tex]
This means the probability that exactly 15 out of the 20 women are employed is approximately 0.0746.
2. At least 10 are employed:
[tex]\[
P(x \geq 10) \approx 0.8725
\][/tex]
Therefore, the probability that at least 10 women are employed outside the home is approximately 0.8725.
3. At most 5 are employed:
[tex]\[
P(x \leq 5) \approx 0.0016
\][/tex]
Hence, the probability that at most 5 out of the 20 women are employed is approximately 0.0016.
4. Between 12 and 14, inclusive, are employed:
[tex]\[
P(12 \leq x \leq 14) \approx 0.4700
\][/tex]
So, the probability that between 12 and 14 women, inclusive, are employed is approximately 0.4700.
5. No more than 9 are employed:
[tex]\[
P(x \leq 9) \approx 0.1275
\][/tex]
Therefore, the probability that no more than 9 women are employed outside the home is approximately 0.1275.
These probabilities provide insights into different scenarios concerning the employment status of women, given the sample size of 20 and the employment rate of 60%.
