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standard deviation of the distribution

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A marketing poll revealed that 45% of Americans say they that they have dinner regularly as a family. You randomly choose 10 American families and ask if they regularly have dinner together as a family.
1. Does this situation meet the binomial requirements? Why or why not? Address the four characteristics in the Key Points.
2. What is the random variable in this problem? i.e., what does X represent and what values can it have?)
3. What is the probability that exactly 4 have regular family dinner?
4. What is the probability that 5 or fewer have regular family dinner?
5. What is the probability that at least 2 have regular family dinner?
6. What is the probability that at most 5 have regular family dinner?
7. What is the mean number of adults out of a sample of 10 that you would expect to have regular family dinner? What is the standard deviation of the distribution?

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This posting offers help with calculating the standard deviation of the distribution.

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Explanations are below:

1. You'll have to check with the "Key Points" from your class, but in general this should be a good but not perfect sample. The poll certainly didn't ask every American, and it certainly didn't pick a perfectly random sample either (this is pretty much impossible). Still, it is likely to provide a good estimate. ...

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