Write the expression for two third of x added to 5

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

2 years ago

Can someone plssss answer these I’m so confused I’m begging u I’l love u foreve

madam [21]

Answer:

22) RT ; angles 2 and 4 are alternate interior angles

23) RT ; angles 1 and 3 are alternate interior angles

24) TV; same-side interior angles (some classes called them consecutive interior angles)

25) RV; same-side interior angles (some classes call them consecutive interior angles)

Step-by-step explanation:

The transversal is the a "line" going through at least 2 others helping to form the angles in question.

22) The line segment going through two line segments that contain angles 2 and 4 is:

RT.

Angles 2 and 4 are alternate interior angles because they happen inside the parallel lines on opposite sides of the transversal at the different intersections of RT and the parallel lines it goes through.

23) The line segment going through at least two line segments that contain angles 1 and 3 is:

RT.

Angles 1 and 3 are alternate interior angles because they happen inside the parallel lines on opposite sides of the transversal at the different intersections of RT and the parallel lines it goes through.

The cool thing about 24 and 25 is that they give you the transversal in the name of the angle.

24) Angles TVR and VTS are being formed by the line segment TV and the parallel line segments that it intersects. TV is the transversal.

Angles TVR and VTS are same side interior angles because they happen inside the parallel lines on the same side of the transerval at the different intersections of TV and the parallel lines it goes through.

25) Angles SRV and RVT are being formed by the line segment RV and the parallel line segments that it intersects. RV is the transversal.

Angles SRV and RVT are same side interior angles because they happen inside the parallel lines on the same side of the transerval at the different intersections of RV and the parallel lines it goes through.