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shtirl [24]
3 years ago
11

The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is

$1600 and the standard deviation is $100. What is the approximate percentage of buyers who paid more than $1900? What is the approximate percentage of buyers who paid less than $1400?What is the approximate percentage of buyers who paid between $1400 and $1600?What is the approximate percentage of buyers who paid between $1500 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1700?What is the approximate percentage of buyers who paid between $1600 and $1900?

Mathematics
1 answer:
marysya [2.9K]3 years ago
8 0

Answer:

(a) 0.14%

(b) 2.28%

(c) 48%

(d) 68%

(e) 34%

(f) 50%

Step-by-step explanation:

Let <em>X</em> be a random variable representing the prices paid for a particular model of HD television.

It is provided that <em>X</em> follows a normal distribution with mean, <em>μ</em> = $1600 and standard deviation, <em>σ</em> = $100.

(a)

Compute the probability of buyers who paid more than $1900 as follows:

P(X>1900)=P(\frac{X-\mu}{\sigma}>\frac{1900-1600}{100})

                   =P(Z>3)\\=1-P(Z

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid more than $1900 is 0.14%.

(b)

Compute the probability of buyers who paid less than $1400 as follows:

P(X

                   =P(Z

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid less than $1400 is 2.28%.

(c)

Compute the probability of buyers who paid between $1400 and $1600 as follows:

P(1400

                              =P(-2

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid between $1400 and $1600 is 48%.

(d)

Compute the probability of buyers who paid between $1500 and $1700 as follows:

P(1500

                              =P(-1

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid between $1500 and $1700 is 68%.

(e)

Compute the probability of buyers who paid between $1600 and $1700 as follows:

P(1600

                              =P(0

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid between $1600 and $1700 is 34%.

(f)

Compute the probability of buyers who paid between $1600 and $1900 as follows:

P(1600

                              =P(0

*Use a <em>z</em>-table.

Thus, the approximate percentage of buyers who paid between $1600 and $1900 is 50%.

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3/5 = 0.60 = 60%



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Answer:

B. 0.5 and 0.2

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Step-by-step explanation:

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3 0
3 years ago
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" () and "tails" () which we write , , etc. For ea
boyakko [2]

Answer:

Some details are missing

Step-by-step explanation:

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails) (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is hht, then R(hht) = 2. Suppose that the random variable X is defined in terms of R as follows: X = 2R² - 6R - 1. The values of X are thus:

Outcome: || Value of X

tht || -5

thh || -5

hth || -5

htt || -5

hhh || -1

tth || -5

hht || -5

ttt || -1

Calculate the probability distribution function of X, i.e. the function Px (x). First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.

Solution

To calculate the probability distribution function of X.

We have to observe the total outcomes to check the number of "Heads (h) " in each outcome.

The first, fourth and, sixth outcome has 1 head (h)

The second, third and seventh outcome has 2 head (hh)

The fifth outcome has 3 head (hhh)

The eight outcome has 0 appearance of h

We then solve the probability of each occurrence

i.e. The probability of having h, hh, hhh and no occurrence of h

This will be represented as follows

P(h=0)

P(h=1)

P(h=2)

P(h=3)

In a coin, the probability of getting a head = ½ and the probability of getting a tail = ½ in 1 toss

Using the following formula

P(X=x) = nCr a^r * b ^ (n-r)

Where n represents total number of toss = 3

r represents number of occurrence

a represents getting a head = ½

b represents probability of getting a tail = ½

1. For h = 0

P(h=0) = 3C0 * ½^0 * ½³

P(h=0) = 1 * 1 * ⅛

P(h=0) = ⅛

2. For h = 1

P(h=1) = 3C1 * ½^1 * ½²

P(h=1) = 3 * ½ * ¼

P(h=1) = ⅜

3. P(h=2) = 3C2 * ½² * ½^1

P(h=2) = 3 * ¼ * ½

P(h=2) = ⅜

4.P(h=3) = 3C3 * ½³ * ½^0

P(h=0) = 1 * ⅛ * 1

P(h=0) = ⅛

It should be noted that when X is -5, h is either 1 or 2 and P(X) = ⅜

When X is -1, h is either 0 or 3 and P(X) = ⅛

The probability distribution function of X is as follows

Values of X || P(x)

-5 || ⅜

1 || ⅛

6 0
3 years ago
What is the slope of the line that passes through (3, −7) and (−1, 1)?
Art [367]

Answer:

<h2>The answer is - 2</h2>

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3, −7) and (−1, 1)

The slope is

m =  \frac{1 -  - 7}{ - 1 - 3}  =  \frac{1 + 7}{ - 4}  =  -  \frac{8}{4}   =  - 2 \\

We have the final answer as

<h3>- 2</h3>

Hope this helps you

3 0
3 years ago
Read 2 more answers
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