1.Suppose that a population is known to be normally distributed with =2,000 and =230. If a random sample of size n=8 isselected, calculate the probability that the sample mean will exceed 2,100.

P(x>2,100)= (Round to four decimal places asneeded.)

2.You have been asked to determine the probability that the contribution margin for a particular product line exceeds the fixed cost of $1440. The total number of units sold is a normally distributed random variable with a mean of 400 and a variance of 900 X~ N(400, 900). The selling price per unit is $10. The total number of units produced is a normally distributed random variable with a mean of 400 and a variance of 1600 Y~ N(400, 1600). The variable production cost is $6 per unit. Production and sales have a positive correlation of 0.50.

What is the probability that the contribution margin for the product line exceeds the fixed cost of $1440?

3.Suppose the life of a particular brand of calculator battery is approximately normally distributed with a mean of 80 hours and a standard deviation of 9 hours.

a. What is the probability that a single battery randomly selected from the population will have a life between 75 and 85 hours?

P(75x85)=

(Round to four decimal places asneeded.)

b. What is the probability that 4 randomly sampled batteries from the population will have a sample mean life of between 75 and 85 hours?

P(75x85)=

(Round to four decimal places asneeded.)

c. If the manufacturer of the battery is able to reduce the standard deviation of battery life from 9 to 8 hours, what would be the probability that 4 batteries randomly sampled from the population will have a sample mean life of between 75 and 85 hours?

P(75x85)=

(Round to four decimal places asneeded.)

4.The time required to a certain specialty coffee at a local coffee shop is uniformly distributed between 40 and 60 seconds. Assuming a customer just ordered one of these specialtycoffees, determine the probabilities described below.

a. What is the probability that the preparation time will be more than 46 seconds?

b. What is the probability that the preparation time will be between 43 and 55 seconds?

c. What percentage of these specialty coffees will be prepared within 51 seconds?

d. What is the standard deviation of preparation times for this specialty coffee at thisshop?

a.P(preparation time more than 46 seconds)=

(Simplify youranswer.)

b.P(preparation time between 43 and 55 seconds)=

(Simplify youranswer.)

c.P(preparation time less than or equal to 51)= %

(Simplify youranswer.)

d. =

(Round to four decimal places asneeded.)