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
Misha Larkins [42]
2 years ago
8

In a recent year, the ACT scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard

deviation of 5.3. Find the probability that a randomly selected high school student who took the math portion of the ACT has a score that is (a) less than 16, (b) between 19 and 24, and (c) more than 26, and (d) identify any unusual events. Explain your reasoning
Mathematics
1 answer:
Natali5045456 [20]2 years ago
6 0

Answer:

a) P(X

And we can find this probability using the normal standard table or excel:

P(z

b) P(19

And we can find this probability with this difference:

P(-0.396

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-0.396

c) P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)

And we can find this probability using the complement rule and the normal standard table or excel:

P(z>0.925)=1- P(Z

d) We can consider unusual events values above or below 2 deviations from the mean

Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5

A value below 10.5 can be consider as unusual

Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7

A value abovr 31.7 can be consider as unusual

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".  

Part a

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

X \sim N(21.1,5.3)  

Where \mu=21.1 and \sigma=5.3

We are interested on this probability

P(X

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

And we can find this probability using the normal standard table or excel:

P(z

Part b

P(19

And we can find this probability with this difference:

P(-0.396

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-0.396

Part c

P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)

And we can find this probability using the complement rule and the normal standard table or excel:

P(z>0.925)=1- P(Z

Part d

We can consider unusual events values above or below 2 deviations from the mean

Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5

A value below 10.5 can be consider as unusual

Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7

A value abovr 31.7 can be consider as unusual

You might be interested in
32 markup 12.5% retail price
Leya [2.2K]

Answer: 36 is the correct answer.

12.5% = .125

32 x .125 = 4

32 + 4 = 36

Step-by-step explanation: I hope this helped you out.

6 0
2 years ago
Thomas drew a line of best fit for the scatter plot as shown. Enter an equation for the line of best fit in slope-intercept form
juin [17]

Answer:

Equation of line best fits the scatter plot is y = -\frac{30}{7} x + 108

Step-by-step explanation:

Let the equation of line be y = mx + c

where m = slope of line and c is the intercept on y -axis

from the graph intercept on y-axis is 108

and the slope of line is given by m = \frac{y_2 - y_1}{x_2 - x_1} where (x_2,y_2) and (x_1,y_1) is the points on line

let, points be (4,96) and (18,36)

on calculating this m = \frac{y_2 - y_1}{x_2 - x_1} = -\frac{30}{7}

Therefore equation of line best fits the scatter plot is y = -\frac{30}{7} x + 108

4 0
3 years ago
Brainliest to correct!
Nimfa-mama [501]

szaeAnswer:

fhx

Step-by-step explanation:ees

ffwsc

4 0
2 years ago
Read 2 more answers
2x + 4) - 5<br> please help!<br> (simplify it)
pochemuha

Answer:

2x-1

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
You are out bottle caps, and decide to use Popsicle sticks instead. You measure them, and they are 15.2 cm tall. How many Popsic
satela [25.4K]
It depends on how many Popsicle sticks you are going to use.So, for example, say that you are using 5 Popsicle sticks for the model. What you do is 15.2 x 5, 15.2 being the height of the sticks and 5 for the number of sticks you are using. The answer will be 76 cm tall.           21                                                                                                                     15.2                                                                                                               x    5                                                                                                                ---------                                                                                                             76.0
3 0
3 years ago
Other questions:
  • The quotient of two and a number, decreased by six
    10·2 answers
  • 5 17/20 write as a decimal
    9·2 answers
  • The slope of line A between (4, 8) and (0, 0) is 2. What is the slope of line A between (-2, -4) and (-4, -8)?
    6·1 answer
  • Three students share 5 peaches equally. How many peaches does each student get?
    10·2 answers
  • What is the value of fraction 1 over 2x3 3.4y when x = 4 and y = 2? 12.8 14.8 25.8 38.8
    7·1 answer
  • Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y End Fraction?
    14·1 answer
  • PLEASE.HELP. 3. In how many years will Mr. Nunez be twice as old as Mr. Springstein?
    10·1 answer
  • In a group of 20 children, there were 8 girls. which is the ratio of girls to boys in simplest form? a: 2:5 b: 8:20 c: 2:3
    11·1 answer
  • Soundtronics is a company that manufactures inexpensive headphones. Due to the high volume some of the headphones are defective
    5·1 answer
  • This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!