A company finds that if they price their product at $ 45, they can sell 110 items of it.

Police use a radar unit is used to measure speeds of cars on a freeway. The speeds are normally distributed with a mean of 90 km

vagabundo [1.1K]

Answer:

A. P(x≥100)=0.1587

B. P(x≤0)≈0

Step-by-step explanation:

A. Cause we know the distribution of the data, the method used to solve it is called "Normalization" and we need to have the Mean and the Standard deviation of the data. The method consist in the following equation

P(x≤a)=P( z=((x-μ)/σ) ≤ b=((a-μ)/σ) )

Considering μ as the Mean and σ as the Standard deviation. At first, we had a probability in the normal distribution with Mean=90 and STD=10 but that kind of exercises is not meant to find that probability directly but by using this process.

After we normalize the probability, now we have a probability in a specific normal distribution that has Mean=0 and STD=1 and the difference with what we had before is that now we are able to use tools to find probabilities in a normal standard distribution. My favorite of them is a chart that show the approximate values of a lot of probabilities (i attached it to this answer). I´m going to explain point A as an example:

We look for the probability that P(x≥100), but we don´t have an easy method to use there, so we normalize:

P(x≥100)=P( (x-μ)/σ ≥ (100-μ)/σ )

P(x≥100)=P( z ≥ (100-90)/10 )

P(x≥100)=P( z ≥ 1 )

And now we are able to use the chart, let me explain: First, the chart only works with P(z ≤ b), so we have to change it with properties of probabilities before using the table.

P(z≥1)=1-P(z≤1)

And finally we use the chart:

the value of P(z≤1) is in the table, we look for the row with +1 and the column with the decimal part (in this case 0) and with coordinates (1,0) there´s the value:

P(z≤1)=0.8413

But we need P(z≥1) so we use the previous equality

P(z≥1)=1-P(z≤1)

P(z≥1)=1-0.8413

P(z≥1)=0.1587

Because P(x≥100)=P(z≥1), our final answer is 0.1587

B. We use the same process to try to understand what the probability of P(x≤0) represents.

P(x≤0)=P(z≤ (0-90)/10)

P(x≤0)=P( z ≤ -9 )

But when we try to look for its value in the chart It isn´t even there, what could it mean?

A normal distribution function is always increasing, that means that "a≤b if and only if P(x≤a) ≤ P(x≤b)". so we conclude:

P(z≤-9) ≤ P(z≤-3) (The lowest probability in the chart)

P(z≤-9) ≤ 0.0013

P(z≤-9) is way lower than 0.0013 (they aren´t even close) but we know that probability is always positive, and because of that:

P(x≤0)=P(z≤-9)≈0

5 0

3 years ago

The price of an item has been reduced by 60% the original price was $20 what is the price of the item now

tester [92]

Answer:

6

Step-by-step explanation:

20 times 0.3 is 6

3 0

3 years ago

Read 2 more answers

Shannon scores 36 points on 6 questions on her test what is the unit rate for one question?

VLD [36.1K]

Answer:

Uh I think 6

Step-by-step explanation:

7 0

3 years ago

Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the

Arturiano [62]

Answer:

4y = -3x - 48

Step-by-step explanation:

y - y1 = m(x - x1)

y1 = -9 x1= -4 m = -3/4

y -(-9) = -3/4(x -(-4)

y + 9 = -3/4(x + 4)

y + 9 = -3/4x -12/4

multiply through by 4

4y + 36 = -3x -12

4y = -3x -12-36

4y = -3x -48 in the form y = mx + c

4 0

2 years ago

What is the stem-and-leaf plot for

Verdich [7]

The stem-and-leaf plot for 29,22,21,6,13,6,17,29,26,9,16,10,25,3,2,23,13,10,7,16,29,30,4,11,7,28,27,22,10 is shown in the image attached below (see attachment).

A stem-and-leaf plot is a table which is used to display a set of data in such a way that, on the left we have the "stem" which displays the first digit or digits of a data value.

On the right, we have the 'leaf' which displays the last digit of the data value.

For example, if we are to represent "25" and "26" on a stem-and-leaf plot, we would have: 2 | 5, 6.

Therefore, the stem-and-leaf plot for 29,22,21,6,13,6,17,29,26,9,16,10,25,3,2,23,13,10,7,16,29,30,4,11,7,28,27,22,10 is shown in the image attached below (see attachment).

Learn more about the stem-and-leaf plot on:

brainly.com/question/8649311

8 0

2 years ago