Show your calculations in detail please.. Suppose that a researcher is conducting a study on fast...

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Show your calculations in detail please..
Suppose that a researcher is conducting a study on fast foodhabits and assumes that 55% of adults prefer hamburger to pizza. Herandomly selects 10 adults and ask whether they prefer hamburger topizza or not. Based on this information, answer the followingquestions.
a) (20 pts) Define the randomvariable (in words) and check whether it is a binomial randomvariable or not and write your conclusion. Explain your answer.
b) (10 pts) What is theprobability that at least 8 adults prefer hamburger?
c) (10 pts) What is theprobability that as most 3 adults prefer hamburger?
d) (15 pts) What is theexpected number of people who prefer hamburger.
e) (15 pts) Calculate the standard deviation of thisrandom variable and interpret it.

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Question aThe random variable here is number of people who preferhamburger to pizzaThe conditions for a random vairable to be a binomail randomvariable is1 The number of trails are fixed Here number of trails is 10So the condition is satiisfied2 Every trail has only two outcomes Here the outcomes are Yesor No when asked about whether they prefer hamburger to pizza ornot So the See Answer

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