### Assignment 4 - The Binomial Distribution

Name: ______________________________

Circle your lab meeting time:
Monday 9:15 Monday 12:15 Monday 3:15 Wednesday 9:15 Wednesday 12:15

1. Find the binomial probability of each possible outcome.

p[0] = ________, p[1] = ________, p[2] = ________, p[3] = ________. p[4] = ________. p[5] = ________.

The S-PLUS code is ___________________.

Verify by hand calculation using the binomial probability formula the probability that exactly two children inherit the disease. (Show work on the back side of the page.)

2. The probability that four or fewer are carriers for the disease is ____________.

The S-PLUS code is ____________________.

3. The probability that thirteen or more athletes would exhibit an improvement with the nasal strip, assuming that there is no benefit is ____________.

The S-PLUS code is ____________________.

4. The mean is ____________ and standard deviation is ____________.

To be within one standard deviation of the mean, the outcome must be in the range from ____________ to ____________ inclusive. This probability is ____________.

The S-PLUS code is ____________________.

5. When `p` is less than __________, the distribution is skewed to the __________.

When `p` is greater than __________, the distribution is skewed to the __________.

When `p` equals __________, the distribution is symmetric.

6. As the sample size increases, the skewness __________.

As the sample size increases, the range of nonnegligible values __________.

As the sample size increases, the proportion of nonnegligible values __________.

As the sample size increases, the general shape resembles a __________ curve.