A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth) Group of answer choices

Answer:

Approximately [tex]0.157[/tex].

Step-by-step explanation:

Let [tex]X[/tex] denote the speed of a car. The question is asking for [tex]P(60 \le X \le 70)[/tex].

That probability is equal to [tex]P(X \le 70)- P(X \le 60)[/tex].

Find each of [tex]P(X \le 60)[/tex] and [tex]P(X \le 70)[/tex] using a [tex]Z[/tex]-table.

Calculate the [tex]Z[/tex] value for [tex]x = 70[/tex] and [tex]x = 60[/tex]:

At [tex]x = 70[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{60 - 55}{5} = 3[/tex].

At [tex]x = 60[/tex], [tex]\displaystyle z = \frac{x - \mu}{\sigma} = \frac{70 - 55}{5} = 1[/tex].

In other words: [tex]P(X \le 70) = P(Z \le 3)[/tex] whereas [tex]P(X \le 60) = P(Z \le 1)[/tex].

Look up [tex]P(Z \le 3)[/tex] and [tex]P(Z \le 1)[/tex] on a [tex]Z[/tex]-table. The question is asking that the answer be rounded to the nearest thousandth. Therefore, keep at least more decimal places than that in intermediate values.

[tex]P(Z \le 3) \approx 0.9987[/tex] and [tex]P(Z \le 1) \approx 0.8413[/tex].

Therefore:

[tex]\begin{aligned}P(60 \le X \le 70) &= P(X \le 70)- P(X \le 60) \\ &= P(Z \le 3) - P(Z \le 1) \approx 0.157\end{aligned}[/tex].

Anybody know the answer to this ?

Match each equation with its graph

Over the period of a year, Julie’s net worth decreased. Which of the following could be true? a. Julie’s assets and liabilities decreased by the same amount. b. Julie’s assets and liabilities increased by the same amount. c. Julie’s assets increased by more than her liabilities. d. Julie’s assets decreased by more than her liabilities. Please select the best answer from the choices provided A B C D

Find the next term of the following sequence. 25,10,4

Write each set of numbers in set-builder and interval notation

X>50

(Sinθ-cosθ)(sinθ+cosθ)=1-2cos^2θ

Which linear regression equation best fits the given points?

(1,18), (4,15), (5,11), (8,9), (10,7), (13,4), (15,0)

yˆ=65x+19.2
yˆ=56x−19.2
yˆ=−65x+18.9
yˆ=−56x−18.9

Brian is playing a carnival game. He is blindfolded while he throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small, "M" for medium, "L" for large, or "XL" for extra-large. The board has 3 small balloons, 5 medium balloons, 2 large balloons, and 2 extra-large balloons. He hits one of the balloons at random and wins a stuffed animal of that size.

A student wants to determine if different types of soil, A and B, affect the propagation of African violets. One hundred leaves from the same variety of African violet were selected. The leaves were then randomly assigned to 50 pots with type A soil and the remaining leaves were put into the 50 pots with type B soil. All of the pots were given the same amount of water and arranged in 10 rows of 10 pots near a window for light. The 50 pots with type A soil were placed closest to the window. At the end of two months, the pots with type A soil had the greatest number of pots with new growth, so the student concluded that soil type A was more effective that soil type B.

Is this a valid conclusion?

Yes, because the leaves were randomly assigned, this evenly distributed the variability in the leaves; therefore, type A soil is more effective than type B soil.

Yes, because the amount of water and light were controlled, this may have reduced the variability in the response; therefore, type A soil is more effective than type B soil.

No, because the pots with type A soil were closest to the window, they received more light, which may have led to the new growth.

No, because only African violets were used, replication was not properly implemented; therefore, we cannot conclude that type A soil was more effective.

Four hot air balloons each descend 295 feet per minute for 7 minutes. Find the total change in altitude for all 4 balloons.
The total change in altitude for all 4 balloons is
(blank) feet.

Calculate the volume

Please show the steps...

Solve this 2 step equation 3x-7=20

What mathematical property is represented by the equation below

c+d=d+c

someone helppp please!!

URGENT HURRY ILL MAKE YOU BRAINIEST IF YOU ANWSER. Mae ling earns a weekly salary of $375 plus a 7.5 commission on sales at a gift shop how much would she make in a work week if she sold 4,600 worth of merchandise

Bobby rode 18 miles in 24 minutes. At this rate, how
many miles did he ride in 4 minutes?

Use the normal distribution to compute probability with technology - Calculator Question Suppose that the annual household income in a region is normally distributed with mean $25,000 and standard deviation $6,000. If the poverty level for the region is at or below $12,000, what percentage of the population lives in poverty? • Round your answer to two decimal places.

Solve for www. -4(w+1) = -24

What is the value of 3-(-2)?

The number of home runs hit by Hank Aaron, the all-time leader, is 755. This
has an order of magnitude of 4
A. True
B. False

Which angles are alternate interior angles explain

need help somebody pleaseee

Write the equation of the line that is parallel to the line y = -3x + 12 and passes through the point (-1, 6). (2 points)

Alex and two friends paid $21.75 to see a movie.How much did each
ticket cost

If {x) = 3x + 2, what is (5)?​

find the measure of 0. (to the nearest tenth).
A) 36.9
B) 38.7
C) 51.3
D) 53.1

Find the equation of the line. Use exact numbers.​

A coat discount 40% off it's regular price. Which value is equivalent to 40%

8x-2 (6x + 4) simplify by using the distributive property

Find the equation of the line that is perpendicular to the given line and passes through the given point.

y = − 1/6x − 5; (14, 0)

The equation is y =______.