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
Jobisdone [24]
3 years ago
9

The distribution of lifetimes of a particular brand of car tires has a mean of 51,200 miles and a standard deviation of 8,200 mi

les. Assuming that the distribution of lifetimes is approximately normally distributed and rounding your answers to the nearest thousandth, find the probability that a randomly selected tire lasts: A) Between 55,000 and 65,000 miles B) Less than 48,000 miles C) At least 41,000 miles D) A lifetime that is within 10,000 miles of the mean
Mathematics
1 answer:
Orlov [11]3 years ago
4 0

Answer:

a) 0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

b) 0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

c) 0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

d) 0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

Step-by-step explanation:

Problems of normally distributed distributions are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 51200, \sigma = 8200

Probabilities:

A) Between 55,000 and 65,000 miles

This is the pvalue of Z when X = 65000 subtracted by the pvalue of Z when X = 55000. So

X = 65000

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

Z = \frac{65000 - 51200}{8200}

Z = 1.68

Z = 1.68 has a pvalue of 0.954

X = 55000

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

Z = \frac{55000 - 51200}{8200}

Z = 0.46

Z = 0.46 has a pvalue of 0.677

0.954 - 0.677 = 0.277

0.277 = 27.7% probability that a randomly selected tyre lasts between 55,000 and 65,000 miles.

B) Less than 48,000 miles

This is the pvalue of Z when X = 48000. So

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

Z = \frac{48000 - 51200}{8200}

Z = -0.39

Z = -0.39 has a pvalue of 0.348

0.348 = 34.8% probability that a randomly selected tyre lasts less than 48,000 miles.

C) At least 41,000 miles

This is 1 subtracted by the pvalue of Z when X = 41,000. So

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

Z = \frac{41000 - 51200}{8200}

Z = -1.24

Z = -1.24 has a pvalue of 0.108

1 - 0.108 = 0.892

0.892 = 89.2% probability that a randomly selected tyre lasts at least 41,000 miles.

D) A lifetime that is within 10,000 miles of the mean

This is the pvalue of Z when X = 51200 + 10000 = 61200 subtracted by the pvalue of Z when X = 51200 - 10000 = 412000. So

X = 61200

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

Z = \frac{61200 - 51200}{8200}

Z = 1.22

Z = 1.22 has a pvalue of 0.889

X = 41200

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

Z = \frac{41200 - 51200}{8200}

Z = -1.22

Z = -1.22 has a pvalue of 0.111

0.889 - 0.111 = 0.778

0.778 = 77.8% probability that a randomly selected tyre has a lifetime that is within 10,000 miles of the mean

You might be interested in
Rewrite 8y - 1/2 (4y - 16) in a different form
worty [1.4K]

Answer:

8y-2y+8=0

6y+8=0

y=8/6=4/3

4 0
3 years ago
What is the behavior of?
GarryVolchara [31]

Answer:

i thin its option 1 or 2 because by looking at the problem it kinda click  after starring at it for awhile

i hope this useful in a way  

5 0
3 years ago
Read 2 more answers
The sum of 14 and a number is equal to 17
GREYUIT [131]
So..... 14 + 3= 17. I think. I mean, this is what I got from what I understand.
5 0
3 years ago
Read 2 more answers
What is 0.0000465 written in scientific notation
Marta_Voda [28]
465•10-5
(That -5 is suppose to be an exponent
6 0
3 years ago
Read 2 more answers
Juan is saving money for a new car. He has already saved $200 and plans to save $25 per week. This situation can be represented
Marina86 [1]
He would have $400 after 8 weeks.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Shereen wishes to advertise her business, so she gives packs of 5 red flyers to each restaurant owner and sets of 10 blue flyers
    6·2 answers
  • Solve: 7x - 5x - 3 = x+4 plz help
    15·1 answer
  • Compare and order the numbers below.
    9·1 answer
  • The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 oun
    11·1 answer
  • Find the circumference of the circle use 3.14
    12·1 answer
  • How do I do this problem
    5·1 answer
  • A division problem is shown below.
    5·1 answer
  • Plz help I’m getting timed
    5·1 answer
  • Consider the following proportion:
    10·2 answers
  • the edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. what is the approximate ar
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!