Question

0 Stats Sp18 Quiz3 name Zhenhaa Wo Suppose you take a "blind" 15 question multiple choice test with 4 answer choices to each question. ("blind" means that you answer the questions without reading them) If you score 10 out of 15 on such test, how many standard deviations is your score above the mean? A. B. C. D. 1 to 2 2 to 3 3 to 4 4 to 5 Use this information to answer questions 2-4. The iPhone cover (below) has 43 customer reviews averaging at 4.5 star rating Assume that standard deviation of all ratings is 0.98 stars. Answer the questions that follow. * 43 customer reviews · Which of the answer choices represents the critical value that should be used to compute 95% c

Answer 1

1.

There are 4 choices in each question out of which 1 is correct. So, probability of getting answer correct = 1/4 = 0.25.

This is a binomial distribution with p = 0.25 and n = 15.

So, for 15 questions, the mean is $\mu = n\cdot p = 15\cdot 0.25 = \mathbf{3.75}$

The standard deviation will be $\sigma = \sqrt{n\cdot p\cdot (1-p)} = \sqrt{15\cdot 0.25\cdot (1-0.25)} = \sqrt{2.8125} \approx \mathbf{1.6771}$

So, a score of 10 out of 15 will be $\frac{x-\mu}{\sigma} = \frac{10-3.75}{1.6771} \approx \mathbf{3.73}$

Answer: C. Score of 10 is 3.73 i.e. 3 to 4 standard deviations above the mean.