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timurjin [86]
2 years ago
7

A set of data has a mean of 56.1. The data follows a normal distribution curve and has a standard deviation of 8.2. Find the pro

bability that a randomly selected value is greater than 67.5
A.
0.0823

B.
1.39

C.
0.9177

D.
–1.08
Mathematics
2 answers:
Whitepunk [10]2 years ago
7 0
Given that mean=56.1 and standard deviation=8.2, P(x>67.5) will be found as follows:
The z-score is given by:
z=(x-μ)/σ
thus the z-score will be given by:
z=(67.5-56.1)/8.2
z=11.4/8.2
z=1.39
thus
P(z=1.39)=0.9177
thus:
P(x>67.5)=1-P(z>0.9177)
=1-0.9177
=0.0823
Answer: A. 0.0823
Tanya [424]2 years ago
4 0

Answer: A.  0.0823


Step-by-step explanation:

Given : Mean \mu=56.1

Standard deviation \sigma=8.2

P(x>67.5) will be found as follows:

The z-score is given by:

z=\frac{X-\mu}{\sigma}

Substitute the values of means ans standard deviation in it, we get

\Rightarrow\ z=\frac{67.5-56.1}{8.2}\\\\\Rightarrow\ z=\frac{11.4}{8.2}\\\Rightarrow\ z=1.39

As

P(z<1.39)=0.9177

thus:

P(X>67.5)=1-P(z<1.39)

⇒P(X>67.5)=1-0.9177

∴P(X>67.5)=0.0823

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aleksandrvk [35]

Answer:

(a) A y P(A) = 0.4 (b) \bar{B} y P(\bar{B})=0.5 (c) \bar{A}∪\bar{B} y P(\bar{A}∪\bar{B}) = 0.9 (d) \bar{A}∩\bar{B} y P(\bar{A}∩\bar{B})=0.2

Step-by-step explanation:

A was defined as the event that a potential customer, randomly chosen, buys from outlet 1 in the original problem statement. We know that B denotes the event that a randomly chosen customer buys from outlet 2. So

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(c) The customer does not buy from outlet 1 is the complement of A, i.e.,  \bar{A}, and the customer does not buy from outlet 2 is the complement of B, i.e.,  \bar{B}, so, the customer does not buy from outlet 1 or does not buy from outlet 2 is  \bar{A}∪ \bar{B} and P(\bar{A}∪ \bar{B}) = P((A\cap B)^{c}) by De Morgan's laws

P((A\cap B)^{c})  = 1-P(A∩B)=1-0.1=0.9

(d) The customer does not buy from outlet 1 is the complement of A, and the customer does not buy from outlet 2 is the complement of B, so we have that the statement in (d) is equivalent to \bar{A}∩\bar{B} and P( \bar{A}∩\bar{B}) = P((AUB)^{c}) by De Morgan's laws, and

P((AUB)^{c}) = 1-P(A∪B)=1-[P(A)+P(B)-P(A∩B)]=1-[0.4+0.5-0.1]=1-0.8=0.2

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