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]
3 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]3 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
Find the value of x<br><br> 3/4 x-4=8
Vesna [10]

Answer: x  =  16

Step-by-step explanation:

Solve for   x  by simplifying both sides of the equation, then isolating the variable.  :)

7 0
3 years ago
Area of a regular hexagon with an apothem of 15 cm
Anton [14]

Answer:

area = 779.4 cm²

Step-by-step explanation:

divide it into 6 equal equilateral triangles. Each corner of a triangle will be 60°.

tan 60° = 15/x

1.7321 = 15/x

x = 8.66 (this is one-half of the base of the triangle)

base = 17.32 cm

area of one triangle = 1/2(17.32)(15) = 129.9 cm²

129.9(6) = 779.4 cm²   (because 6 triangles make up the hexagon)

8 0
2 years ago
How many terms <br> x 2 - 10xy + 3y + y 2 - 1
kicyunya [14]
In algebra a term is a single number or letter so in this 5

x^2
-10xy
3y
y^2
-1

these are all the terms

6 0
3 years ago
Which equations below represent nonlinear functions?
Brilliant_brown [7]
Answer: y = x^2 - 2 does not represent a linear function because the squared exponent above the variable makes that equation quadratic. Quadratic equations look like parabolas on a graph, rather than lines.
4 0
2 years ago
Hi how are you guys 0-0
Mila [183]

Answer:

Im doing quite ok.

Step-by-step explanation:

How have you been?

3 0
3 years ago
Read 2 more answers
Other questions:
  • What value of n makes the equation true?
    5·2 answers
  • A racing car used 255 litres of fuel to complete a 340 km race. On average, how many litres of fuel did the care use every 100 k
    13·1 answer
  • What is it called when Cupid misses his target?
    11·1 answer
  • 4) You are in Las Vegas and need $35 to buy a great steak dinner, but you only have $20. You decide to play roulette to win the
    8·1 answer
  • What is y^(2)-x^(2 ) when y=6 and x=5
    7·2 answers
  • Included side between
    7·1 answer
  • Evaluate the problem<br><br> 3.14(6 × 4 + 6^2)
    13·2 answers
  • Arrange the hyperbolas in increasing order of the horizontal widths of their asymptote rectangles.
    9·1 answer
  • Which expression is equivalent to (3x2+3x−3)−(6x2−4x−2)?
    8·1 answer
  • Please i need help :
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!