# Calculate probabilities with the binomial distribution

Every day, 17% of the U.S. population with Internet access checks the weather in that way. For a sample of 5 people taken on any given day:

1. Construct a table of the binomial probability distribution for this case.
2. View this information using a histogram.
3. Calculate the mean, variance, and standard deviation for this distribution.
4. Calculate the probability that at least 3 people in the sample checked the weather that day.

According to a recent infographic (NAMI: National Alliance on Mental Illness, n.d.), “1 in 20 U.S. adults experience serious mental illness” in the United States. If a random sample of 20 students is selected from a large school district,

1. Construct a table of the binomial probability distribution for this case.
2. View this information using a histogram.
3. Calculate the mean, variance, and standard deviation for this distribution.
4. If 3 of the students were diagnosed with serious mental illness, would this be a signal about the school district having a problem with mental health among the students being above the national score?