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Luda [366]
3 years ago
9

Statistics Probability

Mathematics
1 answer:
andriy [413]3 years ago
4 0

Answer:

Explained below.

Step-by-step explanation:

Denote the variable as follows:

M = male student

F = female student

Y = ate breakfast

N = did not ate breakfast

(a)

Compute the probability that a randomly selected student ate breakfast as follows:

P(Y)=\frac{n(Y)}{N}\\\\=\frac{198}{330}\\\\=0.60

(b)

Compute the probability that a randomly selected student is female and ate breakfast as follows:

P(F\cap Y)=\frac{n(F\cap Y)}{N}\\\\=\frac{121}{330}\\\\=0.367

(c)

Compute the probability a randomly selected student is male, given that the student ate breakfast as follows:

P(M|Y)=\frac{n(M\cap Y)}{n(Y)}\\\\=\frac{77}{198}\\\\=0.389

(d)

Compute the probability that a randomly selected student ate breakfast, given that the student is male as follows:

P(Y|M)=\frac{n(Y\cap M)}{n(M)}\\\\=\frac{77}{154}\\\\=0.50

(e)

Compute probability of the student selected "is male" or "did not eat breakfast" as follows:

P(M\cup N)=P(M)+P(N)-P(M\cap N)\\\\=\frac{n(M)}{N}+\frac{n(N)}{N}-\frac{n(M\cap N)}{N}\\\\=\frac{n(M)-n(N)-n(M\cap N)}{N}\\\\=\frac{154+132-77}{330}\\\\=0.633

(f)

Compute the probability of "is male and did not eat breakfast as follows:

P(M\cap N)=\frac{n(M\cap N)}{N}\\\\=\frac{77}{330}\\\\=0.233

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Step-by-step explanation:

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The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542. Suppos
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Answer:

(a) P(X > $57,000) = 0.0643

(b) P(X < $46,000) = 0.1423

(c) P(X > $40,000) = 0.0066

(d) P($45,000 < X < $54,000) = 0.6959

Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

<em>Let X = annual salaries in the metropolitan Boston area</em>

SO, X ~ Normal(\mu=$50,542,\sigma^{2} = $4,246^{2})

The z-score probability distribution for normal distribution is given by;

                      Z  =  \frac{X-\mu}{\sigma }  ~ N(0,1)

where, \mu = average annual salary in the Boston area = $50,542

            \sigma = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

    P(X > $57,000) = P( \frac{X-\mu}{\sigma } > \frac{57,000-50,542}{4,246 } ) = P(Z > 1.52) = 1 - P(Z \leq 1.52)

                                                                     = 1 - 0.93574 = <u>0.0643</u>

<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

    P(X < $46,000) = P( \frac{X-\mu}{\sigma } < \frac{46,000-50,542}{4,246 } ) = P(Z < -1.07) = 1 - P(Z \leq 1.07)

                                                                     = 1 - 0.85769 = <u>0.1423</u>

<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

    P(X > $40,000) = P( \frac{X-\mu}{\sigma } > \frac{40,000-50,542}{4,246 } ) = P(Z > -2.48) = P(Z < 2.48)

                                                                     = 1 - 0.99343 = <u>0.0066</u>

<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.

(d) Probability that the worker’s annual salary is between $45,000 and $54,000 is given by = P($45,000 < X < $54,000)

    P($45,000 < X < $54,000) = P(X < $54,000) - P(X \leq $45,000)

    P(X < $54,000) = P( \frac{X-\mu}{\sigma } < \frac{54,000-50,542}{4,246 } ) = P(Z < 0.81) = 0.79103

    P(X \leq $45,000) = P( \frac{X-\mu}{\sigma } \leq \frac{45,000-50,542}{4,246 } ) = P(Z \leq -1.31) = 1 - P(Z < 1.31)

                                                                      = 1 - 0.90490 = 0.0951

<em>The above probability is calculated by looking at the value of x = 0.81 and x = 1.31 in the z table which gave an area of 0.79103 and 0.9049 respectively</em>.

Therefore, P($45,000 < X < $54,000) = 0.79103 - 0.0951 = <u>0.6959</u>

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3 years ago
I need help on this problem is the answer A
vladimir1956 [14]
Well, I'm not completely sure, because I don't know the formal definition
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Here's what I can tell you about the choices:

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This is definitely a corner of the feasible region.
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B).  (3.5, 0)
This is ON the boundary line between the feasible and non-feasible
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C).  (8, 0)
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So tome, this looks like probably the best answer.

D).  (5, 3)
This is definitely a corner.  It's the point of intersection (the solution)
of the two equations that are the first two constraints. 

The feasible region is a triangle.
The three vertices of the triangle are  (0,8) (choice-A), 
(0,-7) (not a choice),  and  (5,3) (choice-D) .
region is a triangle

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3 years ago
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