The following 5 questions are based on this information. A survey indicates that the proportion of girls in the total youth in the United States is 51% (p=0.51).

Wewill take a random sample of 400 U.S. youths.

1)The sampling distribution of p, the sample proportion of U.S.youths who are girls, is:

2)The standard error (SE) of p is

3)What is the probability that a random sample of 400 U.S. youth will provide a sample proportion (p) that is within 0.03 of the population proportion (p)?

4)What is the probability (rounded) that a random sample of 400 U.S youth will provide a sample proportion (p) that is within 0.07 of the population proportion (p)?

5) Say, you took a random sample of 400 U.S. youth, and found out that the sample proportion (p) for this sample to be 0.42. IS THIS A RARE FIND?

please show step by step, equations . dumbproof it to the best of your ability

please dont type like this P[ |X(bar)-| <25] =P[ |(X(bar)-)/(/sqrt(n))| <25>