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
Zepler [3.9K]
3 years ago
6

The speeds of cars on a given i street we are normally distributed with a mean of 72 miles per hour and a standard deviation of

3.2 miles per hour. What percent of drivers are traveling between 70 and 80 miles per hour based on this distribution
Mathematics
1 answer:
Ostrovityanka [42]3 years ago
3 0

Answer: 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

Step-by-step explanation:

Let X be a random variable that represents the speed of the drivers.

Given: population mean : M = 72 miles ,

Standard deviation: s= 3.2 miles

The probability that the drivers are traveling between 70 and 80 miles per hour based on this distribution:

P(70\leq X\leq 80)=P(\frac{70-72}{3.2}\leq \frac{X-M}{s}\leq\frac{80-72}{3.2})\\\\= P(-0.625\leq Z\leq 2.5)\ \ \ \ \ [Z=\frac{X-M}{s}]\\\\=P(Z\leq2.5)-P(Z\leq -0.625)\\\\\\ =0.9938-0.2660\ \ \ [\text{Using p-value calculator}]\\\\=0.7278

Hence, 72.78% of the drivers are traveling between 70 and 80 miles per hour based on this distribution.

You might be interested in
20 earth pounds on the moon
tatiyna
20 earth pounds on the moon would equate to 3.31 pounds.
4 0
3 years ago
Whats the answer to this problem
vlabodo [156]
The answer would be to the right since after you factor the equation out the 9 is positive
8 0
3 years ago
It is estimated that 0.54 percent of the callers to the Customer Service department of Dell Inc. will receive a busy signal. Wha
stira [4]

Using the binomial distribution, it is found that there is a 0.8295 = 82.95% probability that at least 5 received a busy signal.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • 0.54% of the calls receive a busy signal, hence  p = 0.0054.
  • A sample of 1300 callers is taken, hence n = 1300.

The probability that at least 5 received a busy signal is given by:

P(X \geq 5) = 1 - P(X < 5)

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{1300,0}.(0.0054)^{0}.(0.9946)^{1300} = 0.0009

P(X = 1) = C_{1300,1}.(0.0054)^{1}.(0.9946)^{1299} = 0.0062

P(X = 2) = C_{1300,2}.(0.0054)^{2}.(0.9946)^{1298} = 0.0218

P(X = 3) = C_{1300,3}.(0.0054)^{3}.(0.9946)^{1297} = 0.0513

P(X = 4) = C_{1300,4}.(0.0054)^{4}.(0.9946)^{1296} = 0.0903

Then:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0009 + 0.0062 + 0.0218 + 0.0513 + 0.0903 = 0.1705.

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.1705 = 0.8295

0.8295 = 82.95% probability that at least 5 received a busy signal.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1

6 0
1 year ago
234.A<br><br> 124/B<br><br> 136.B<br><br> 156.D
makvit [3.9K]
I think it’s D. 156 degrees
7 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%7B2%7D%5E%7Bn%7D%20%20%3D%20226%20%20" id="TexFormula1" title=" {2}^{n} = 226 " alt=" {2
Rudik [331]
N equals to 7.82 (to 2 decimal places)

5 0
3 years ago
Read 2 more answers
Other questions:
  • Nezzie is shopping for items for her daycare because the store is having a sale where everything in the store is 10% off. Nezzie
    9·2 answers
  • The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i
    7·1 answer
  • If two lines have the same slope, they are _______.
    14·1 answer
  • 9._
    8·1 answer
  • Consider the open sentence 2x + 3___x^2 + 2^2 ( show all your work )
    6·1 answer
  • The probability that a person catches a cold during the cold and flu season is 0.4. assume that 10 people are chosen at random.
    7·1 answer
  • Match each word to the appropriate example using the expression 5a + 9b - 4.
    5·2 answers
  • How to solve 700/2,5 with steps pleaaaase​
    14·1 answer
  • 6. this solid has curved sides. all cross sections parallel to the base are squares measuring 3 units on each side. the height f
    6·1 answer
  • Mandisa draws a rectangle to represent the area of her yard. The area can be represented by 10x2 – 13x – 14.What expressions can
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!