1. For this problem, please use the appropriate notations, show the formula you used, the intermediate values used, and your final answer.

In a study of brand recognition, 95% of consumers recognized Pepsi (based on data from Total Research Corporation). Find the probability that if 12 people are randomly selected:

b. (2) exactly 10 will recognize Pepsi.

c. (4) at most 4 will recognize Pepsi

d. (4) between 7 and 11 inclusive will recognize Pepsi

e. (4) more than 9 will recognize Pepsi

f. (3) If 20 people are randomly selected and the brand recognition is still 95%, what is the probability that exactly 17 people will recognize Pepsi?

BUSA 251 Week 6 ProblemsPage 2

For the following problem, draw a diagram of the normal distribution, label the coordinates, position the mean, standard deviation, random variable and/or z-score and shade the area of interest .

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 75 and a standard deviation of 11 points.

a. (5) what is the probability that a student scores between 70 and 85?

b. (5) 17% of the students will earn a grade higher than what minimum score? c. (7) What is the probability that a student scores between 60 and 68?

11. It is very difficult for small businesses to be successful. The small Business Administration estimates that 30 percent will dissolve or go bankrupt within two years. A sample of 50 new businesses is selected. (Hint: use the normal approximation to the binomial). Make sure to clearly label the scales and mark the values of the important points on the graph as well as show the shaded area of interest. Please, meticulously show all your work.

a. (6) What is the probability that at most 11 new businesses will go bankrupt?