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
melisa1 [442]
3 years ago
9

The opera theater manager believes that 27'% of the opera tickets for tonight's show have been sold. If the manager is right, wh

at is the probability that the proportion of tickets sold in a sample of 741741 tickets would differ from the population proportion by less than 4%4%
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
7 0

Answer:

0.9858 = 98.58% probability that the proportion of tickets sold in a sample of 741 tickets would differ from the population proportion by less than 4%.

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.

For a proportion p in a sample of size n, we have that \mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}

In this problem, we have that:

p = 0.27, n = 741

So

\mu = 0.27

\sigma = \sqrt{\frac{0.27*0.73}{741}} = 0.0163

What is the probability that the proportion of tickets sold in a sample of 741 tickets would differ from the population proportion by less than 4%.

This is the pvalue of Z when X = 0.27 + 0.04 = 0.31 subtracted by the pvalue of Z when X = 0.27 - 0.04 = 0.23. So

X = 0.31

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

Z = \frac{0.31 - 0.27}{0.0163}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 0.23

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

Z = \frac{0.23 - 0.27}{0.0163}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability that the proportion of tickets sold in a sample of 741 tickets would differ from the population proportion by less than 4%.

You might be interested in
Which is a true statement about the data shown in the tables?
myrzilka [38]

Answer:

D

Step-by-step explanation:

Neither table os a linear relation

8 0
3 years ago
Read 2 more answers
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents t
Neko [114]

Answer:

A)   A[p(t)] = 36πt²

B)   7234.56 square units

Step-by-step explanation:

               

<u>Given functions</u>:

\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}

<u>Part A</u>

To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):

\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}

<u>Part B</u>

Given

  • t = 8 minutes
  • π = 3.14

Substitute the given values into the equation for A[p(t)} found in part A:

\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}

Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.

4 0
2 years ago
Read 2 more answers
The weekly milk order for the Tranquility Hotel includes 40 gallons of low- fat milk and 15 gallons of chocolate milk. What is t
Zigmanuir [339]

Answer:

15:40

Hope it helps!

3 0
3 years ago
I need help with this and explain how to do it please!!<br> 6x - 4z
Troyanec [42]

Answer:

you should know you dont need help so do it by yourself. if you want the awnser you should know or you just dont pay attention in class.1234567890 is your awnser

4 0
3 years ago
I need help is due today!!!:Cool tees is having a back to school sale where all t-shirts are discounted by 15%. Joshua wants to
Softa [21]

Answer:

$64.5745

Step-by-step explanation:

You had to do this:

9.99+11.99+11.99+21.00+21.00=75.97

 x     =     85

75.97      100        85*75.97=6457.45

100x=6457.45

6457.45/100= 64.5745

8 0
3 years ago
Other questions:
  • Given frequent itemset l and subset s of l, prove that the confidence of the rule "s’ =&gt; (l - s’)" cannot be more than the co
    13·1 answer
  • Fgh is a right triangle
    11·1 answer
  • UgH y’all help !!!!<br><br> I’ll mark you brainliest ONLY if you get it RIGHT.
    9·2 answers
  •  A school is planning a field trip to a theme park. A ticket to the park costs ​$21. For a group of 50 or​ more, there is a 12​%
    6·1 answer
  • If a polynomial function f(x) has roots 6 and square root of 5, what must also be a root of f(x)?
    8·1 answer
  • ???? i am confusion ????
    13·2 answers
  • The dimensions of a triangle are represented by the functions shown. Which function represents the area of the triangle, g(x) =
    7·2 answers
  • 5
    8·1 answer
  • Write an equation of the line in slope-intercept form (0,-3) (3,-2)​
    11·2 answers
  • zaheeda scored 9 goals in netball matches .At this rate , about how msny goals will she score in ten games​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!