1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
erica [24]
3 years ago
11

On a particular stretch of highway, the State Police know that the average speed is 62 mph with a standard deviation of 5 mph. O

n a busy holiday weekend, the police are concerned that people travel too fast. So they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. Use central limit theorem to calculate
Mathematics
1 answer:
makkiz [27]3 years ago
5 0

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.

In this problem:

  • Mean of 62 mph, hence \mu = 62.
  • Standard deviation of 5 mph, hence \sigma = 5.
  • Sample of 50 cards, hence n = 50, s = \frac{5}{\sqrt{50}} = 0.7071

The probability of a sample of 50 cars recording an average speed of 66 mph or higher is <u>1 subtracted by the p-value of Z when X = 66</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{66 - 62}{0.7071}

Z = 5.66

Z = 5.66 has a p-value of 1.

1 - 1 = 0.

There is a 0% probability of a sample of 50 cars recording an average speed of 66 mph or higher.

A similar problem is given at brainly.com/question/24663213

You might be interested in
The table shows how the number of sit-ups marla does each day has changed over time. at this rate how many sit-ups will she do o
DENIUS [597]
The number of situps form an AP with first term (a) = 17 and common difference (d) = 4

Tn = a + (n - 1)d
T12 = 17 + (12 - 1) x 4 = 17 + 11(4) = 17 + 44 = 61

Therefore, she will do 61 situps on day 12.
5 0
3 years ago
Read 2 more answers
NEED HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ra1l [238]

Answer:

122+42x= 2( 61+21x)

4x+16x+24 = 4(5x+6)

24x+48-3x = 21x+48

3x+39-2x = x+29

Step-by-step explanation:

7 0
3 years ago
Factor completely.<br> 3x^2+30x+75=
mamaluj [8]
You write the problem as a mathematical expression
3x^2 + 30x + 75 =
Factor: 3 out of 3x^2 + 30x + 75.

3 (x2 + 10x + 25)

Factor using the perfect square rule.
And then your answer should be 3 ( x + 5) ^2
7 0
3 years ago
Read 2 more answers
Ike's igloo sold 501 ice cream cones today.They sold half as many chocolate ice cream cone as vanilla ones. How many of each wer
34kurt

Answer:

Chocolate cones = x = 167 cones

Vanilla cones = y = 334 cones

Step-by-step explanation:

Let

The number of Chocolate cones = x

Vanilla cones = y

Ike's igloo sold 501 ice cream cones today.

x + y = 501.... Equation 1

They sold half as many chocolate ice cream cone as vanilla ones.

x = 1/2y

x = y/2

Cross multiply

y = 2x

We substitute 2x for y in Equation 1

x + 2x = 501

3x = 501

x = 501/3

x = 167

Solving for y

y = 2x

y = 2 × 167

y = 334

Therefore,

The number of

Chocolate cones = x = 167 cones

Vanilla cones = y = 334 cones

4 0
2 years ago
Which ratio is equelivent to 24 : 28?​
Vaselesa [24]

Answer:

Hello there!

The correct answer is 18:21.

Hope This Helps You!

Good Luck :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • Joseph invested $16,000 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawa
    13·1 answer
  • It takes Dariya 35 seconds to download 5 songs from the Internet. How can the number of seconds it would take Dariya to download
    13·2 answers
  • Which of the following is a example of a infinite decimal?
    8·1 answer
  • What is 2.11 in a mixed number simplified
    15·2 answers
  • What times what equals 90 ?
    8·2 answers
  • Is this line liner<br> why or why not<br> SOMEBODY HELP ASAP
    14·1 answer
  • You mow the lawn to earn your allowance. Each time you mow the lawn you earn \$12$12dollar sign, 12. Write an equation for the n
    14·1 answer
  • PLEASE HELP ASAP 30 POINTS
    7·1 answer
  • A bag contains 3 blue marbles, 1 green marble, and 4 orange marbles. A marble is pulled out of the bag at random. The probabilit
    12·1 answer
  • Which ordered pair is a solution to the system of linear equations? 2x 3y= 6 –3x 5y = 10 (0,2) (2,0) (3,2) (2,3)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!