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
pantera1 [17]
3 years ago
6

When Aria commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 28 minutes and a st

andard deviation of 4.5 minutes. Out of the 262 days that Aria commutes to work per year, how many times would her commute be between 32 and 35 minutes, to the nearest whole number?
Mathematics
1 answer:
MrRa [10]3 years ago
6 0

Answer:

Her commute would be between 32 and 35 minutes 33 times.

Step-by-step explanation:

Problems of normally distributed samples 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 problem, we have that:

\mu = 28, \sigma = 4.5

Proportion of days in which the commute is between 32 and 35 minutes:

This is the pvalue of Z when X = 35 subtracted by the pvalue of Z when X = 32.

X = 35

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

Z = \frac{35 - 28}{4.5}

Z = 1.555

Z = 1.555 has a pvalue of 0.94.

X = 32

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

Z = \frac{32 - 28}{4.5}

Z = 0.89

Z = 0.89 has a pvalue of 0.8133.

0.94 - 0.8133 = 0.1267

Out of 262 days:

Each day, 0.1267 probability

0.1267*262 = 33

Her commute would be between 32 and 35 minutes 33 times.

You might be interested in
And insurance agent receives 15% of the cost of each insurance policy she sells how much does the agent receive for a policy ths
hammer [34]

In this question there are several important information's provided. Using these information's it is easy to get the answer to the question asked. Firstly it is already informed that the insurance agent gets a commission of 15% of the policy price for every policy sold. The agent sells a policy of $300.

Now we can write the equation as:

15% of $300 = [(15/100) * 300] dollars

                    = ( 15 * 3) dollars

                    = 45 dollars

So the agent gets a commission of $45 for selling a policy worth $300

3 0
2 years ago
Read 2 more answers
What is the volume of the right rectangular prism?
Zepler [3.9K]

Answer:

Volume = 308cm^{3}

Step-by-step explanation:

Volume of a rectangular prism = Height * Width * Depth

Sub in the three values and solve

V = 11 * 7 * 4

V = 308cm^{3}

8 0
3 years ago
Translate this problem to an equation and solve. The product of 2 positive consecutive even integers is 48. What is the smaller
bonufazy [111]
Let x represent the first even integer: x = 2(k) → y = 2k
Let y represent the second even integer: y = 2(k + 1)  → y = 2k + 2

   x  ·     y        = 48
(2k) · (2k + 2) = 48
 4k² + 4k - 48  = 0
 4(k² + k - 12)  = 0
4 (k + 3)(k - 2) = 0
k = -3, k = 2  (Note: POSITIVE integers so k = -3 is ruled out)

x = 2k → x = 2(2) → x = 4
y = 2(k + 1) → y = 2(2 + 1) → y = 2(3) → y = 6

The smaller number (x) is 4
        


8 0
3 years ago
A parallelogram is _____ a quadrilateral.<br><br> A) Sometimes<br><br> B) Never<br><br> C) Always
Vlad [161]
C) Always anything more you want to know?
6 0
3 years ago
Read 2 more answers
Which fraction is greater? 3/4, 2/3​
marta [7]
It’s 3/4
3/4 is 75% when converted while
2/3 is 67% when converted
Meaning 3/4 is great than 2/3
3 0
3 years ago
Read 2 more answers
Other questions:
  • The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width.
    11·2 answers
  • A sphere and a cone have the same volume. each figure has a radius of 3 inches.
    15·1 answer
  • 46 POINTS!!!
    10·1 answer
  • If two functions are one-to -one that means that the are also _____ of each other
    8·1 answer
  • Three friends paid 26.25 to see a movie how much did each ticket cost
    7·1 answer
  • What is the slope of the line passing through (-3, 5) and (5, -3)?​
    8·2 answers
  • 10) the LAST ONE Use Distributive Property and Combine Like Terms to simplify the expression below HELP PLZ PLZ PLZ
    13·2 answers
  • ZA and ZB are supplementary angles. If m_A
    7·1 answer
  • This is URGENT please help!
    12·2 answers
  • Is the leg on the bottom the same size as the one on the right?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!