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
babymother [125]
2 years ago
14

5. MOUNTAIN BIKING On a mountain bike trip along the Gemini Bridges Trail in Moab, Utah, Nabuko stopped on the

Mathematics
1 answer:
USPshnik [31]2 years ago
6 0

Answer:

Try to watch math antics for that

You might be interested in
The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili
Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

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

By the Central Limit Theorem

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

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

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

Z = \frac{77 - 74}{1.2274}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 71

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

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

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

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0
3 years ago
What is 2x + 45?<br><br> Plz help, Wanna T.a.l.k?
Gre4nikov [31]
X= 22.5 get the x by itself by dividing by 2
8 0
2 years ago
Read 2 more answers
Indicate whether classical, empirical, or subjectiveprobability should be used to determine each of the following:
Snezhnost [94]

Answer:

Indicate whether classical, empirical, or subjective probability should be used to determine each of the following probabilities.

Step-by-step explanation:

a)  The probability that a certain model will win the beauty contest

is an example of which type of probability?

B - Classical  

b) "The probability that next card in the deck will be black" is an example of which type of probability?

 

B- Classical

c) "The probability that there will be at least 16 tropical storms this  summer" is an example of which type of probability?

B-Subjective  

d)  "There is a 0.30 probability of randomly selecting a student who has a part- time job " is an example of which type of probability?

A- Subjective

5 0
3 years ago
Which of the binomials below is a factor of this trinomial?
Leokris [45]

Answer:

x+5 is the factor..

Step-by-step explanation:

xsquare + (8+5)x + 40

or, xsquare +8x+5x+40

or, x(x+8)+5(x+8)

(x+5)(x+8)

4 0
3 years ago
A car rents for ​$35 per day plus 18cents¢ per mile. you are on a daily budget of ​$71. what mileage will allow you to stay with
Butoxors [25]
200 miles
$71-$35=$36 left in budget
$36/.18 per mile= 200 miles
6 0
3 years ago
Other questions:
  • Which point is collinear to the point (0, 0)?
    12·1 answer
  • The weight, in pounds, of a newborn baby tt months after birth can be modeled by the function W(t)=1.25t+6.W(t)=1.25t+6. What is
    15·1 answer
  • An empty box is shaped like a rectangular prism. The box has a base area of 9/10 square foot and a height of 1/3' foot. How much
    5·1 answer
  • Assuming each car has 4 tires, how many cars can you service if you have 120 tires? (Y=Mx+B)
    11·1 answer
  • A bicycle wheel with diameter 16 inches rides over a screw in the street. The screw is on level ground before it
    14·1 answer
  • 2369 divided by 6= t
    6·2 answers
  • What is the solution to: Create two whole number division problems that have a quotient of 9 and a remainder of 5. justify which
    13·1 answer
  • Solve for the missing angle measures.
    8·1 answer
  • How do you write 5.13 × 10–4 in standard form?
    15·1 answer
  • 50 POINTS!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!