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
aleksklad [387]
3 years ago
7

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If th

e variable is normally distributed, what is the probability that a randomly selected town will have a homicide rate greater than 8?
Mathematics
1 answer:
zlopas [31]3 years ago
5 0

Answer:

P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)  

And we can find this probability with the complement rule:  

P(Z>-1)=1-P(Z  

Step-by-step explanation:

Previous concepts  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem  

Let X the random variable that represent the average homicide rate for the cities of a population, and for this case we know the distribution for X is given by:  

X \sim N(10,2)  

Where \mu=10 and \sigma=2  

We are interested on this probability  

P(X>8)  

And the best way to solve this problem is using the normal standard distribution and the z score given by:  

z=\frac{x-\mu}{\sigma}  

If we apply this formula to our probability we got this:  

P(X>8)=P(\frac{X-\mu}{\sigma}>\frac{8-\mu}{\sigma})=P(Z>\frac{8-10}{2})=P(Z>-1)  

And we can find this probability with the complement rule:  

P(Z>-1)=1-P(Z  

You might be interested in
What is the mode and median of 1,2,1,3,3,5,3,4,5,4,3,2,5,3,1.​
tankabanditka [31]

<em><u>hope</u></em><em><u> </u></em><em><u>it</u></em><em><u> </u></em><em><u>helps</u></em><em><u> </u></em><em><u> </u></em><em><u>uh</u></em><em><u> </u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em><em><u>!</u></em><em><u>!</u></em><em><u>!</u></em><em><u>!</u></em>

8 0
3 years ago
Jerry can eat 24 hot dogs in 6 minutes. They want to know how many minutes (m) it would take them to eat 35 hot dogs if they can
scZoUnD [109]

Answer: 8 minutes and 45 seconds or 8.75 minutes

Step-by-step explanation:

Find hot dogs per minute

24/6=4 hot dogs per minute

35/4=8.75

So jerry needs 8 minutes and

60x0.75= 45 seconds

6 0
3 years ago
Which two shapes can be classified as parallelograms?
Deffense [45]
Actually there are three shapes that can be classified as a parallelogram.

Square, Rectangle, and Rhombus
3 0
3 years ago
Read 2 more answers
According to an NRF survey conducted by BIGresearch, the average family spends about $237 on electronics (computers, cell phones
Usimov [2.4K]

Answer:

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is 0.0537.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is 0.0023.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is 0.1101.

Step-by-step explanation:

We are given that according to an NRF survey conducted by BIG research, the average family spends about $237 on electronics in back-to-college spending per student.

Suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54.

Let X = <u><em>back-to-college family spending on electronics</em></u>

SO, X ~ Normal(\mu=237,\sigma^{2} =54^{2})

The z score probability distribution for normal distribution is given by;

                                 Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean family spending = $237

           \sigma = standard deviation = $54

(a) Probability that a family of a returning college student spend less than $150 on back-to-college electronics is = P(X < $150)

        P(X < $150) = P( \frac{X-\mu}{\sigma} < \frac{150-237}{54} ) = P(Z < -1.61) = 1 - P(Z \leq 1.61)

                                                             = 1 - 0.9463 = <u>0.0537</u>

The above probability is calculated by looking at the value of x = 1.61 in the z table which has an area of 0.9463.

(b) Probability that a family of a returning college student spend more than $390 on back-to-college electronics is = P(X > $390)

        P(X > $390) = P( \frac{X-\mu}{\sigma} > \frac{390-237}{54} ) = P(Z > 2.83) = 1 - P(Z \leq 2.83)

                                                             = 1 - 0.9977 = <u>0.0023</u>

The above probability is calculated by looking at the value of x = 2.83 in the z table which has an area of 0.9977.

(c) Probability that a family of a returning college student spend between $120 and $175 on back-to-college electronics is given by = P($120 < X < $175)

     P($120 < X < $175) = P(X < $175) - P(X \leq $120)

     P(X < $175) = P( \frac{X-\mu}{\sigma} < \frac{175-237}{54} ) = P(Z < -1.15) = 1 - P(Z \leq 1.15)

                                                         = 1 - 0.8749 = 0.1251

     P(X < $120) = P( \frac{X-\mu}{\sigma} < \frac{120-237}{54} ) = P(Z < -2.17) = 1 - P(Z \leq 2.17)

                                                         = 1 - 0.9850 = 0.015

The above probability is calculated by looking at the value of x = 1.15 and x = 2.17 in the z table which has an area of 0.8749 and 0.9850 respectively.

Therefore, P($120 < X < $175) = 0.1251 - 0.015 = <u>0.1101</u>

5 0
3 years ago
গ. মুক্তিযােদ্ধাদের আক্রমণে পাকিস্তানিদের কয়টি স্পিডবােট ডুবে গিয়েছিল?
Ad libitum [116K]

Answer:

3)7

Step-by-step explanation:

3 0
2 years ago
Other questions:
  • 7. An investment account pays 3.9% interest compounded semi-annually. If
    12·1 answer
  • When Rafael emptied his pockets, e found he had a total of $3.50 in quarters and nickels. If he had 8 more quarters that nickels
    5·1 answer
  • Kayla notices that she can buy snacks and candy in bulk at the grocery store. The snacks she wants to buy weigh 1 kilogram. Writ
    13·2 answers
  • Solve the following system of equations.<br><br> 2x+y=3<br> x=2y-1
    10·2 answers
  • Determine if line AB is tangent to the circle. If so, then explain why.
    14·1 answer
  • PLZ HELP <br> What is the best interpretation of P(3) =12
    7·2 answers
  • The ____ ____ separates the places larger than 1 from those that are fractions of 1, such as tenths, hundredths, etc.
    14·2 answers
  • In Vindales wig shop 1/4 of the wigs are blonde and 1/4 of wigs are brunette. What fraction of the wigs are either blonde or bru
    7·1 answer
  • Can someone help me with these?
    6·1 answer
  • The graphs of f(x) = 5* and its translation, g(x), are
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!