## Statistics: Reference Chapter 1-9: http://ryanrapini.com/media/statistics/Statistics_for_Engineers.pdf

Question 10.

Consider the following experiment; simultaneously toss a fair coin and independently roll a fair die

1. Write out the 12 outcomes that comprise the sample space for this experiment.

The toss of the coin = (Head, tail)

Throw of the die = {1,2,3,4,5,6}

The probability of tossing a coin and getting a head or a tail would be equal that is =1/2

P(AB) = P(A)P(B) = ½ X1/2 =1/4

From the sample space of twelve, it can be deduced that 3 of the twelve likely events comprise AB, and that; P(AB) = P(A) + P(B) – P(AB) =3/4. That is nine of twelve equally likely events makes AB

1. Let X be a random variable that takes the value of 1 if the coin shows heads and the value of 0 if the coin shows tails. Let Y be the random variable that takes the value of the up face of the tossed die. And let Z = X+Y. construct the probability mass function for Z

For independent variables

 PXY X1=-1 X2 = 0 X3 = 1 PY(yj) Y1=-1 1/12 1/6 1/4 1/2 Y2=0 1/18 1/9 1/6 1/3 Y3=1 1/36 1/18 1/12 1/6 PX(Xk) 1/6 1/3 1/2

For joint probability function

 P) X1=1 X2 = 0 P Y1=-1 1/12+1/4+1/36+1/12=4/9 1/6+1/18=2/9 2/3 Y2=0 1/18+1/6=2/9 1/9 1/3 P(Xk) 2/3 1/3
1. Find the mean of Z
1. Find the variance for Z

Question 1

The number of customers entering a certain restaurant in any given day is approximately normally distributed with a mean of 40 and a standard deviation of 10. Find the probability that during a given day;

1. At least 40 customers arrive P(X>=40) = 0.5
2. No more than 45 customers arrive P(X=<45)

P(X

P(X 0.6915

Question 7.

1. Calculation of the pooled estimate of the standard deviation
1. Use the turkeys multiple comparison procedure to compare the mean rates of penetration for the three drill bits. Identify the means that differ. Use α=0.01.

This represents a 99% level of confidence.

For a two sided system the degree of freedom can be calculated from

0.99/2=0.495