For a statistics project, Zenon decided to investigate if students at his school prefer name-brand potato chips to store-brand potato chips. He prepared two identical bowls of chips, filling one with name-brand chips and the other with store-brand chips. Then, he selected a random sample of 30 students, had each student try both types of chips in random order, and recorded which type of chip each student preferred. Assume that 50% of students at Zenon’s school prefer the name-brand chips. Let X = the number of students in the sample that prefer the name-brand chips.   a, Calculate the mean and standard deviation.   b. Interpret the standard deviation      (c)  Justify the distribution of X is approximately normal.     (d) Calculate the probability that 19 or more of the students will prefer the name-brand chips.

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  1. For a statistics project, Zenon decided to investigate if students at his school prefer name-brand potato chips to store-brand potato chips. He prepared two identical bowls of chips, filling one with name-brand chips and the other with store-brand chips. Then, he selected a random sample of 30 students, had each student try both types of chips in random order, and recorded which type of chip each student preferred. Assume that 50% of students at Zenon’s school prefer the name-brand chips. Let X = the number of students in the sample that prefer the name-brand chips.

 

a, Calculate the mean and standard deviation.

 

b. Interpret the standard deviation




     (c)  Justify the distribution of X is approximately normal.





    (d) Calculate the probability that 19 or more of the students will prefer the name-brand chips.  






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