-10, -3, -1, 4, 7, 15, 19, 32
a.) First find the mean:
mean = 63/8 = 7.875
b.) Now let�s find the variance:
= 1288.875 / 7 = 184.125
c.) Last, square root the number and find the standard deviation:
?184.125 = 13.569
2.) Let X ~ N(4, 5). Answer the following questions.
a.) Draw a picture of the distribution of X.
Normal curve with mean of four and a standard deviation of 5.
b.) Find P(X < 2).
= 0.3446
c.) Find P(X > 13).
= 0.0359
d.) Find P(3 < X < 10).
= 0.4642
e.) Find P(X > -5).
= 0.9641
3.) Machine A makes parts whose lengths are approximately normal distributed with a mean of 4.6 mm and a standard deviation of 0.1 mm. Machine B makes parts whose lengths are approximately normally distributed with a mean of 4.9 mm and a standard deviation of 0.2 mm. Suppose that you have a box of parts which you believe are from Machine A, but you�re not sure. You will test your hypotheses by randomly selecting one part from the box.
a.) What are the two hypotheses to be tested?
Ho: Parts are from Machine A
H1: Parts are from Machine B
b.) Draw the distributions for the lengths of parts under Ho and H1. For both parts, label the x-axis from 4.2 to 5.2. Include all important features.
c.) i.) Suppose that you get a length of 4.8 mm. In your sketch for part b.), label the p-value region on your graph.
ii.) What is the p-value for your region?
0.0228
d.) What is your decision at the 0.01 level? At the 0.10 level? (In other words, are the results Statistically Significant at ? = 0.01 and ? = 0.10?) Why or why not?
SS at 0.10 level but not at 0.01 level.
4.) Let X ~ U(-2, 4). Answer the following questions.
a.) Draw the Distribution of X.
Box structure ranging from -2 to 4 with a height of 1/6.
b.) What is P(-4 < X < -2)?
0
c.) What is P(-1 < X < 1.5)?
0.4167
d.) What is the mean of this distribution?
1