Find the mean, variance and standard deviation of the buyers who buy white flip-flops.

Binomial Distribution Problems P3301
A store sells womens flop-flops in eight different colors. Despite the different selections 50% of all flip-flops sold are white. Suppose 30 buyers are selected at random:
1.Find the mean, variance and standard deviation of the buyers who buy white flip-flops.
2.Plot a graph of this binomial using R and save it to a Word file. Include the graph.
3.In probability theory there is a rule that says
In any dataset the probability that an observation is within k standard deviations of the mean (i.e. the interval ) is at least as long as
Find the probability that the number of white shoe purchases is in the interval ( ) and compare this probability to that given by the above rule.
4.Suppose two groups of 30 customers are randomly chosen. What is the probability of at least one group has 15 people that buy white shoes?
Due to stricter training requirements, fewer big fires, higher paying jobs in cities, and changes in society, the number of volunteer firefighters is declining. According to one source, approximately 75% of all firefighters in the U.S. are volunteers and this total number has declined by 10% over the past two decades. Suppose 32 U.S. firefighters are chosen at random.
1.Graph the distribution.
2.Find the probability that exactly 22 of these firefighters are volunteers.
3.Find the probability that more than 25 of these firefighters are volunteers.
4.Suppose that 17 of the firefighters are volunteers. Is there any evidence to suggest that the proportion of volunteer firefighters has decreased Justify your answer.
5.Suppose that 50 firefighters are randomly chosen from the West and 50 firefighters are randomly chosen from the Northeast, What is the probability that 40 of the firefighters in each group will be volunteers?
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