Normal Distribution
Authored by Lim Hui
Mathematics
12th Grade
CCSS covered
Used 3+ times
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10 questions
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1.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
1. Suppose X~N(4,9), the standard deviation of X is
2
3
4
9
Answer explanation
The number 9 is the variance of X.
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Suppose X~N(4,9), probability P(X > 5.5) can be found using GC by keying in
a) Normalcdf(5.5,E99, 4, 9)
b) Normalcdf(5.5,E99, 2, 9)
c) Normalcdf(5.5,E99, 4, 3)
d) Normalcdf(5.5,E99, 4, 81)
Answer explanation
You need to remember to give standard deviation instead of variance in the GC keystrokes.
Tags
CCSS.HSS.ID.A.4
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
In Discrete Random Variables chapter, when X is a discrete random variable, to find P(X>=5), we have P(X>=5) = 1 - P(X<=4). Can we do so for if X were to be following a normal distribution?
Yes
No
Answer explanation
No, you cannot. If you do that, you will miss out removing the probability where X is between 4 and 5, since X is a continuous random variable now. You will need just key in normalcdf (5, E99, mean, standard deviation) to find the probability.
Tags
CCSS.HSS.ID.A.4
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Let H be heights of students. Find the probability that the heights of three students is at least 4m. The expression should be
P ( 3H > 4)
P (3H >= 4)
P (H1 + H2 + H3 > 4)
P (H1 + H2 + H3 >= 4)
Answer explanation
There are three students, so there should be 3 variables. At least means including the number 4 as well.
Tags
CCSS.HSS.CP.B.7
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
The heights of students, H, follow a normal distribution with mean 1.1 and variance 0.4. Find the probability that the heights of three students is more than 4m. The probability is P(H1+H2+H3 > 4). What is the distribution of H1+H2+H3?
N (3 x 1.1, 3 x 0.4)
N (3 x 1.1, 9 x 0.4)
N (3 x 1.1, 3 x 0.16)
N (3 x 1.1,
3 x sq rt (0.4) )
Answer explanation
0.4 is already the variance, not standard deviation. The format is N (mean, variance).
Var (H1+H2+H3) = Var(H1) + Var(H2) + Var(H3)
=3 Var(H)
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Let X~N (4, 9) and Y~N(16, 25), where X and Y are independent variables.
Var (Y-X) is
25 - 9 = 16
25 + 9 = 34
5 - 3 = 2
5 + 3 = 8
Answer explanation
Variance only have addition. DO NOT subtract.
7.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Chickens and turkeys are sold by weight. The masses, in kg, of the chickens and turkeys are modelled as having independent normal distributions with the following means and standard deviation.
Chicken C : mean 2.2, standard deviation 0.5
Turkey T : mean 10.5, standard deviation 2.1
Chickens and sold at $3 per kg and turkeys are sold at $5 per kg.
Which expression represents the cost of 3 chickens and 2 turkeys?
3C + 2T
C1+C2+C3+T1+T2
3(3C)+5(2T)
3(C1+C2+C3)+5(T1+T2)
Answer explanation
There are 5 animals, thus there should be 5 variables. The cost is multiplied to the total weight of the type of farm animals.
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