(Section 6.5) Sampling distribution of the mean
with ,
,
n = 25
Note that we must assume that our "symmetric" distribution
is approximately normal,
since n is only 25.
7.
(Section 4.5) Binomial distribution
with n = 8, p = .1
(a)
(b)
.1488 + .03307 = .18187
(c)
P(X = 8) = .00000001
(d)
np = 8(.1) = 0.8
8.
(Section 6.6) Sampling distribution of the proportion
with n = 125, p = .10
Note: This problem could also be solved with the
binomial distribution.
(a)
(b)
9.
(Section 1.7) Types of data
(a)
Numerical, discrete
(b)
Categorical
(c)
Categorical
(d)
Numerical, continuous
(e)
Numerical, continuous
(f)
Categorical ("Yes" or "No")
10.
(Section 2.1) Stem-and-leaf plots
*Also see section 3.2 (shape, mode)
(a)
The shape is approximately symmetric.
(b)
mode = 21 (it appears 3 times)
11.
(Section 6.6) Sampling distribution of the proportion
with n = 50, p = .70
Note: This problem could be solved with the
binomial distribution as well.
(a)
(b)
12.
(Section 3.2) Central tendency/Variation
(a)
,
Q_{2} = 6
(b)
s = 6.15088,
s^{2} = (6.15088)^{2} = 37.83332
(c)
range = max - min = 12 - (-8) = 20,
IQR = Q_{3} - Q_{1} = 8.5 - (-1) = 9.5
(d)
13.
(Section 3.4) Empirical rule
The empirical rule states that 95% of the data falls within
2 standard deviations of the mean.
Therefore, the distance from 15 to 35
(which is 35 - 15 = 20) should be 4 standard deviations.
So we have 4s = 20; s = 5.
14.
(Section 4.5) Binomial distribution
with n = 5, p =.80
(a)
(b)
P(X = 0) = .00032
(c)
np = 5(.8) = 4
15.
(Section 6.1) Normal distribution
with ,
(a)
P(-1.25 < Z < 2.5) = .88814048
(b)
(c)
"Faster" means less time. 10% have quicker (smaller) times,
and 90% have slower (larger) times. This is the 10^{th}
percentile.
16.
(Section 4.5) Binomial distribution
with n = 20, p = .04
(a)
P(X = 0) = .442002
(b)
17.
(Section 6.5) Sampling distribution of the mean
with ,
,
n = 100
Note: If students buy
tickets (or less)
on the average, then the 250 tickets would be enough for
for the 100 students.
18.
(Section 6.1) Normal distribution
with
,
(a)
If 75% of all workers earn more than you, then your wage
is the 25^{th} percentile.
per hour
(b)
(c)
19.
(Section 6.2) Normal probability plots
(a)
Based on the shape of the boxplot and histogram, the data
looks non-normal. Both plots are highly right-skewed.
(b)
The normal probability plot is far from a straight line.
This data does NOT look normal.