-12, -4, -2, 6, 11, 18, 21, 42
a.) First find the mean:
10
b.) Now let�s find the variance:
=2050/7 = 292.857
c.) Last, square root the number and find the standard deviation:
= ?292.857 = 17.11
2.) Let X ~ N(3, 6). Answer the following questions.
a.) Draw a picture of the distribution of X.
A normal curve with a mean of three and a standard deviation of six.
b.) Find P(X < 1).
= 0.3707
c.) Find P(X > 15).
= 0.0228
d.) Find P(3 < X < 10).
= 0.377
e.) Find P(X > -8).
= 0.9664
3.) Machine A makes parts whose lengths are approximately normal distributed with a mean of 4.5 mm and a standard deviation of 0.1 mm. Machine B makes parts whose lengths are approximately normally distributed with a mean of 5.1 mm and a standard deviation of 0.2 mm. Suppose that you have a box of parts which you believe are from Machine B, 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 B
H1: Parts are from Machine A
b.) Draw the distributions for the lengths of parts under Ho and H1. For both parts, label the x-axis from 4.2 to 5.5. Include all important features.
c.) i.) Suppose that you get a length of 4.7 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 NSS at 0.01 level.
4.) Let X ~ U(-4, 8). Answer the following questions.
a.) Draw the Distribution of X.
Box structure ranging from -4 to 8 and having a height of 1/12.
b.) What is P(-6 < X < -4)?
0
c.) What is P(-1 < X < 6.5)?
0.625
d.) What is the mean of this distribution?
2