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
jek_recluse [69]
3 years ago
8

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op

eration, and low cost. Suppose the maximum speed of a moped is normally distributed with mean value 46.7 km/h and standard deviation 1.75 km/h. Consider randomly selecting a single such moped. (a) What is the probability that maximum speed is at most 50 km/h? (Round your answer to four decimal places.) (b) What is the probability that maximum speed is at least 47 km/h? (Round your answer to four decimal places.) (c) What is the probability that maximum speed differs from the mean value by at most 1.5 standard deviations? (Round your answer to four decimal places.)
Mathematics
1 answer:
Mashcka [7]3 years ago
3 0

Answer:

a) P(X<50)=0.9827

b) P(X>47)=0.4321

c) P(-1.5<z<1.5)=0.8664

Step-by-step explanation:

We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.

a) This means we have to calculate P(x<50).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

z=\dfrac{X-\mu}{\sigma}=\dfrac{50-46.7}{1.75}=\dfrac{3.7}{1.75}=2.114\\\\\\P(X

b) We have to calculatee P(x>47).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

z=\dfrac{X-\mu}{\sigma}=\dfrac{47-46.7}{1.75}=\dfrac{0.3}{1.75}=0.171\\\\\\P(X>47)=P(z>0.171)=0.4321

c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5

z=\dfrac{(\mu+1.5\sigma)-\mu}{\sigma}=\dfrac{1.5\sigma}{\sigma}=1.5

So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):

P(-1.5

You might be interested in
What is the simplified version of the expression [(5-1)^2+3^2]/(30 / 6)
VARVARA [1.3K]

Answer:

Exact form is \frac{16}{5} +\frac{3^2}{5}

the decimal form is 5

Step-by-step explanation:

4 0
3 years ago
Eva and her children went into a restaurant and where they sell hotdogs for $5 each and tacos for $2.50 each. Eva has $30 to spe
eimsori [14]

2 hotdogs and 12 tacos

3 0
3 years ago
MOREEEEEEEEEEEEEEEEEEE POINTSSSSSSSSSSSSSSSSSSSSSS
WINSTONCH [101]

Answer:

Thank you so much

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the range of the data?
Ghella [55]
O
..............…....
5 0
3 years ago
Help me please ASAP, I will give Brainliest!!
Flura [38]
Equation: 18(20) * 7 or 18(20) x 7
4 0
3 years ago
Read 2 more answers
Other questions:
  • A square has a side of 6.25 feet. What is the area in square feet? Round to the correct significant digits.
    10·2 answers
  • here is a rectangle ABCD the length of the rectangle is increased by 10% the width of the rectangle is increased by 5% find the
    8·1 answer
  • 572 to the nearest hundred
    5·2 answers
  • 6r = 3(r - 4) - r<br> need help asap!
    7·2 answers
  • You and a friend each roll a die to see who goes first in a board game. what is the probability that at least one of you rolls a
    13·1 answer
  • If 1 16 oz can cost. $1 how much is 8 40oz cans
    11·1 answer
  • What is the value of 16(3) − wx16(3) - wx, when w = 20 and x = 1212
    7·1 answer
  • Name the angle relationship.<br> please help
    10·1 answer
  • Identify any solutions to the system given below.
    12·2 answers
  • Which is the solution set of the compound inequality 3.5 x minus 10 greater-than negative 3 and 8 x minus 9 less-than 39
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!