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Consider a town where the average age of all individuals is 35.6 years old with a standard deviation of 13.7 years. Suppose you were to randomly select 50 individuals from this town as part of a study.  What is the probability that the average age of the 50 individuals in your study would be less than 30 years old and greater than 40 years old?

A study was conducted that found 46.9% of all smartphone users in the US had an iPhone. Suppose you were to randomly sample 40 US smartphone users. What is the probability that at least 18 of them had an iPhone? Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

A study was conducted that found 15% of all US adults have some form of student loan debt. Suppose you were to randomly sample 100 US adults. What is the probability that at anywhere from 23 to 40 of them would have student loan debt? Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

A study was conducted that found 83% of all teenagers in the US own at least one video game console. Suppose you were to randomly sample 30 US teenagers. What is the probability that exactly 24 of them would own at least one video game console? Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

Determine if the following situation satisfies all of the conditions required for a binomial probability experiment. If it does, then specify how each of the conditions are satisfied. If it does not, then specify which conditions are not met.Make sure to provide sufficient justification for your answers by stating how each condition is met in context of the scenario given.    Scenario: A student walks into class after not showing up the week before and finds out there is a multiple choice quiz in class that day. Since they were not in class during the previous week, all they can do is randomly guess on each question. There are 12 questions on the quiz and all of the questions have 3 possible answers (A,B, or C). The number of correct answers on the quiz will be recorded. 

A local landscaping company was running a promotional offer to plant drought resistant trees for homeowners, and the survival rate for those plants has been 91% in the past. Christine just bought a new home and she is looking to hire the company to plant 10 drought resistant trees in her yard. What is the probability that at most 9 of those trees survive? Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23.

The average height for an NCAA Division 1 men’s basketball player is 77 inches. Assume this data is normally distributed with a standard deviation of 8 inches. Use this information to answer the following question.  What is the probability that a randomly selected NCAA D1 men’s basketball player is at most 72 inches tall? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type in 0.65. 

According to the Bureau of Labor Statistics, in 2019 U.S. households spent an average of $386.92 per month on food. Assume this data is normally distributed with a standard deviation of $112. Use this information to answer the following question.  What Z-score would correspond to a household that spent an average of $555 on food per month in 2019? Make sure to round your answer to 2 decimal places; i.e. if your answer was 87.654321 then you would type in 87.65. 

Suppose you have a standard deck of 52 playing cards and you randomly select 1 card and record whether or not the card that you drew was a “club”. You then return to the card back to the deck and repeat this process a total of 6 times so that you end up drawing 6 cards total. Find the probability that more than 2 of the 6 cards that you drew were clubs.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23. Note: In a standard deck of playing cards, 13 of them are clubs and 39 of them are not. 

Suppose you are carrying out a hypothesis test at the