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The queuing time at an airline check-in has a population mean h = 13 minutes and variance o2 = 16 minutes2. Suppose that n = 27 passengers were randomly selected from this population. They were interviewed and reported the queued times. Let x̄ defines the sample mean of n observations. Answer the followings:

a) Define your random variable X.

b) Define the sampling distribution of sample mean (indicate a reason and give the name of the distribution, the parameters and sketch it.

c) What is the probability that a sample mean is at most 11 minutes. Please skecth the problem and show all details of your answer.

d) Suppose that for n = 27 passengers, the sample mean is observed as x̄= 10 minutes. Based on part c, can we claim that the population mean queuing time is less than 13 minutes.

e) Construct a 95% acceptance region for sample mean of queing time (i.e., u + za x f) Interpret the result obtained in parte and skecth the control chart.

Two ladybugs sit on a rotating disk. Ladybug 1 is halfway between ladybug 2 and the axis of rotation.

What is the angular speed of ladybug 1?

1. The same as the angular speed of ladybug 2

2. One half as the angular speed of ladybug 2

3. Double the speed of ladybug 2

4. None of these

What is a private network? Discuss it’s range.

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.

Figure P2.2