Homework SourseQUESTION 1 Students scores are averaging 85 with a standard
QUESTION 1
Students’ scores are averaging 85 with a standard deviation of 4. The 96% will have a value close to:
60
70
85
93
6 points
QUESTION 2
When a sampling distribution of Xbar should be considered?
Path: p
Words:4
6 points
QUESTION 3
If the number of calories on a slice of strawberry pie is in average 160 with a standard deviation of 10 then the probability of having a slice of apple pie with more than 180 calories is the closest to:
80%
40%
4%
-15%
6 points
QUESTION 4
The X value range is:
-1% to +1%
-infinite to +infinite
-100 to +100
0 to 1
4 points
QUESTION 5
The expected value of a discrete random variable is:
n*p*q
x*p(x)
(x - µx)2 p(x)
p(x)
4 points
QUESTION 6
When one is using the standard normal distribution, P(Z < 0) is:
-.5
1
-
50%
4 points
QUESTION 7
In few lines explain what z-scores are and why they are useful?
Path: p
Words:0
4 points
QUESTION 8
as the sample size gets larger, the standard deviation of the sample mean also gets larger and larger.
True
False
4 points
QUESTION 9
A standard normal distribution has a standard deviation of ____and a mean of ____
zero, zero
zero, one
one, zero
one, one
4 points
QUESTION 10
Which of the following is a valid probability value for a discrete random variable?
101%
99.999%
1.35
-2.63%
4 points
QUESTION 11
A student\'s grade on an examination was transformed to a z value which is negative. Therefore, we know that he scored
higher than 16% of the class
lower than at least 45% of the class
higher than 45% of the class
above the mean but below the median
above the 3rd quartile
6 points
QUESTION 12
In a large automobile manufacturing company, the mean life of hybrid motors is normally distributed with a mean of 100,000 miles and a standard deviation of 10,000 miles. If a random sample of 144 motors is selected, what is the probability that the sample mean will be below 99,000 miles per year is close to:
-10%
35%
50%
11%
6 points
QUESTION 13
What is the expected value of a lottery ticket where there are only 1 chance in 10 millions of winning the grand prize of $5 Million, and 100,000 in 10 millions chances of winning $100?
Give a brief explanation.
Path: p
Words:0
6 points
QUESTION 14
The area under the normal curve between z = -2 and z = -3 is _______than the area under the normal curve between z = 3 and z = 4.
equal to
less than
greater than
A, B, or C above depending on the value of the mean
6 points
QUESTION 15
The customers spent in average $80 with a standard deviation of $5.
The probability of a customer to spend $80 or more is _____________
-48%
85
50%
100%
6 points
QUESTION 16
The earnings set of data has an average of $75 with a standard deviation of $5. The probability of having more than $60 is closer to:
NOTE: if you understand the concept you don\'t really need to do any computation.
35%
99%
50%
60%
4 points
QUESTION 17
The total area under a normal distribution is = 1
True
False
4 points
QUESTION 18
If the X + 2*s.d. from the mean, the area under the curve (relative to the mean) is close to:
.9500
1.96
.2000
.4800
increases, exponential
6 points
QUESTION 19
If the sampled population has mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of Xbar for n = 16 are
48 and 4
48 and 1
12 and 4
48 and 16
4 and 1
6 points
QUESTION 20
If the mean value is 20 with a stdev of 1. The best approximation for the low 15% will be:
18
15
22
20
| 60 | ||
| 70 | ||
| 85 | ||
| 93 |
Solution
Q1.
P ( Z < x ) = 0.96
Value of z to the cumulative probability of 0.96 from normal table is 1.751
P( x-u/s.d < x - 85/4 ) = 0.96
That is, ( x - 85/4 ) = 1.75
--> x = 1.75 * 4 + 85 = 92.004 ~ 93
Q3.
P(X > 180) = (180-160)/10
= 20/10 = 2
= P ( Z >2) From Standard Normal Table
= 0.0228 ~ 4
Q20.
P ( Z < x ) = 0.15
Value of z to the cumulative probability of 0.15 from normal table is -1.036
P( x-u/s.d < x - 20/1 ) = 0.15
That is, ( x - 20/1 ) = -1.04
--> x = -1.04 * 1 + 20 = 18.964 ~ 18
