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
Sedaia [141]
3 years ago
8

At a large university, the mean amount spent by students for cell phone service is $58.90 per month with a standard deviation of

$3.64 per month. Consider a group of 44 randomly chosen university students. What is the probability that the mean amount of their monthly cell phone bills is more than $60?
Mathematics
1 answer:
zhenek [66]3 years ago
4 0

Answer:

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

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 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.

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.

In this problem, we have that:

\mu = 58.90, \sigma = 3.64, n = 44, s = \frac{3.64}{\sqrt{44}} = 0.54875

What is the probability that the mean amount of their monthly cell phone bills is more than $60?

This is 1 subtracted by the pvalue of Z when X = 60. So

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

By the Central Limit Theorem

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

Z = \frac{60 - 58.90}{0.54875}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

2.28% probability that the mean amount of their monthly cell phone bills is more than $60

You might be interested in
If the exterior sides of two adjacent angles are opposite rays, then the angles are _____ angles.
elena-s [515]
The correct answer is B. Supplementary

That is the basic definition of what supplementary angles are and can be found in any textbook.
4 0
3 years ago
Read 2 more answers
Marsha earn $25 per hour up to 36 hours; after this,she is paid double time. In one particular week she earned $1550.00 .how man
mel-nik [20]

Answer: Marta worked 13 hours overtime.

Step-by-step explanation:

1): You do 25 x 36 to get the amount of money she can make before she starts to make double.

36 x 25 = 900

2): Minus $900 from $1550

$1550 - $900 = $650

3): Divide $650 by $50

$650 / $50 = 13 hours worked overtime

7 0
3 years ago
A low-wattage radio station can be heard only within a certain distance from the station. On the graph below, the circular regio
zmey [24]
For the answer to the question above, 
My answer in which <span>equation represents the boundary for the region where the station can be heard</span> would be multiple choice letter <span>D. (x + 6)^2 + (y + 1)^2 = 16
I hope my answer helped you solve your problem, Have a nice day!</span>
5 0
3 years ago
The measures of two complementary angles are in the ratio 8:1. how many degrees are in the larger angle?
djverab [1.8K]
Since the measures of the two angles are in the ratio 8:1, this means the bigger angle's is 8x and the smaller angle is x. Since they are complementary, they add to 90°, so you create the equation 8x+x=90°. This can be simplified to 9x=90°. Then, you divide 90 by 9 to get 10. This means x=10. Next, you replace x with 10 to find the measure of the bigger angle. 8x10=80, so the larger angle is 80°.
4 0
3 years ago
The measure of an angle is 28 degrees less than its supplement. find the supplement
barxatty [35]

Supplementary angles measure 180°. Make an equation:

x+(x+28) = 180

Subtract 28 to leave the variable in the parentheses alone:

x+(x+28-28) =180-28 \\ x+x = 152

Add the 2 x's together:

x+x = 2x

Your new equation is:

2x=152

Divide both sides by 2 to leave the variable alone

\frac{2x}{2} = \frac{152}{2}  \\ \\ x = 76

The supplement measures 76°

8 0
4 years ago
Other questions:
  • The change in the value of an account when given to the nearest dollar?
    11·1 answer
  • (5,-2)and (9,6)write the equationof the line slope intercept form and then standard form that passes through given points show w
    7·1 answer
  • Simplify i to the 37th power<br> A-1<br> B- -1<br> C- -i<br> D- i
    8·1 answer
  • If f(x) = {ln x for 0 &lt; x less than or equal to 2
    10·1 answer
  • Is 3/4 multiplied by 7/10 less than 3/4?
    9·2 answers
  • If y varies jointly as x and x = 33 when y = 22, find x when y = 32
    15·1 answer
  • There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three
    5·1 answer
  • What is the point-slope form of a line with slope 3/2 that contains the point
    14·1 answer
  • How do you describe the square root of a rational number​
    6·2 answers
  • When multiplying decimals, how do you find the number of
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!