1. Tallula's Medical Supplies lnc. manufactures pacemakers, A pacemaker has a mass of 48 g The probabilty that a pacemaker is detective is 25%. The number of defective pacemakers in a fixed number of pacemakers can be modeled by a binomial random varidble. 
   
   the a normal distribution to approximate the probability that in a production run of 300 pacemakers, less than 74 are defective. 
   
   Give your answer 3s a decimal to four places. 
   
   Remember lo use a continuity correction.

A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly. 12. Six of these cards will be selected at random. Let X = the number of red cards observed in the set of six selected cards. Which of the following probability distributions is appropriate for modeling the random variable X? A) The Normal distribution with mean 3 and variance 1.22. B) The binomial distribution with parameters n= 6 and p=0.5. C) The binomial distribution with parameters n = 10 and p = 0.5. D) None of the above.

The Lakeside Coffee Shop morning customer load follows a normal distribution. The mean number of customers is 60 and the standard deviation is 15.

1. Determine the probability that the number of customers tomorrow will be 50. (3 marks)
2. If the store gets more than 70 customers, they need to have a fourth staff member working. What is the probability that they will need that fourth person tomorrow? (3 marks)
3. If the number of customers falls below 42, then two staff members are sufficient. What are the chances only two workers are required tomorrow? (3 marks)

Problem 5. (10 points) Steve sells cars at a local dealership. The number, X, of cars he sells on a given day is uncertain, but an estimate of the probability distribution for X is: Cars sold Probability 0.2 0.45 0.25 0.2 0.45 0.25 (a) What is the mean number of automobiles Steve expects to sell on a given day?