Question

Crave is a large subscription-based internet streaming service for movies

and television shows. Suppose the proportion of Saskatchewanians who have a Crave

subscription is 0.15. Suppose the population of Rosetown, Saskatchewan is 2700 people. What is the probability that between 14% and 17% of people in Rosetown, Saskatchewan have a Crave subscription? Round your standard deviation to 4 decimal places.

Note: In your answer, please show all of the following:
1) The distribution your random variable follows
2) The probability you are asked to calculate

3) Any tricks you use

4) Your rounded z-score (remember to round your z-score to 2 decimal places)

5) Your final probability

Answer 1

1). My random variable of number of people in Rosetown who subscribe to Crave follows a Binomial distribution.

2). The Probability I was asked to calculate is the proportion of people in Rosetown who subscribed to Crave.

3) Here, since n=2700, is quite large, I shall use the Normal approximation to Binomial distribution.

4). For a Normal approximation, we know that

where is the given subscription rate ie 0.15 and n=2700.

We are asked to find out the prob that p is between 0.14 and 0.17.

Therefore when p=0.14,   

  

  

   which will yield(rounded to two figures)

When p=0.17,

  

  

  

Therefore the Z scores are -1.46 to 2.91.

5)The final probability:

  

Which equal to finding the probability

the probability that between 14% and 17% of people in Rosetown, Saskatchewan have a Crave subscription=0.926