Homework #4
ME 236
I. Review Questions (Not Due)
1. True or False:
a. Using the t distribution presumes that the population is normally distributed.
b. At the same level of confidence, the Student-t value is always less than or equal to the z
value.
c. The t table is used in place of the z table when the population standard deviation is
unknown.
d. The shape of the t distribution depends on the number of measurements in the sample.
2. Fill in the missing values. SKETCH the z or t distribution, AND graphically demonstrate the
probabilities and ranges.
a. P( -__________ ≤ z ≤ +__________ ) = 0.75 (both unknowns have same magnitude)
b. P(-2.35 ≤ z ≤ -0.88 ) = _____________
c. P( t ≤ __________ ) = 0.75 (50 degrees of freedom)
d. P( -0.695 ≤ t ≤ 3.055 ) = __________ (12 degrees of freedom)
II. Homework (Due)
Turn in the following problems from the book, plus the extra Problem 4-A ON THE NEXT
PAGE.
4-1, 3, 4, 6, 7
4-A. You are designing an automatic coin counter that stacks 50 pennies at a time to be placed
in coin wrappers. You plan on measuring the height of the stack to determine the number of
coins, but are concerned as to how accurate the method will be.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Sums
Thickness,
x
(mm)
1.48
1.47
1.38
1.42
1.54
1.56
1.44
1.52
1.47
1.56
1.42
1.52
1.60
1.47
1.50
1.47
1.44
1.45
1.52
1.42
1.49
1.39
1.51
1.53
1.43
1.48
1.45
1.61
1.47
1.55
44.56
(x − x)2
0.00003
0.00024
0.01110
0.00427
0.00299
0.00558
0.00206
0.00120
0.00024
0.00558
0.00427
0.00120
0.01315
0.00024
0.00022
0.00024
0.00206
0.00125
0.00120
0.00427
0.00002
0.00909
0.00061
0.00200
0.00306
0.00003
0.00125
0.01554
0.00024
0.00317
0.09735
You measure the thickness of 30 pennies, with the data listed
below.
a. Based on this data, estimate the height of a stack of 50 pennies.
How accurate is your estimate, at 95% confidence?
b. What percentage of pennies from the population have
thicknesses of at least 1.34 mm?