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
muminat
3 years ago
7

The time needed to complete a final examination in a particular college course is normallydistributed with a mean of 80 minutes

and a standard deviation of 10 minutes. Answer thefollowing questions.a. What is the probability of completing the exam in one hour or less?b. What is the probability that a student will complete the exam in more than 60 minutesbut less than 75 minutes?c. Assume that the class has 60 students and that the examination period is 90 minutesin length. How many students do you expect will be unable to complete the exam inthe allotted time?
Mathematics
1 answer:
Artist 52 [7]3 years ago
4 0

Answer:

a) 0.023

b) 0.286

c) 10 students will be unable to complete the exam inthe allotted time.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 80 minutes

Standard Deviation, σ = 10 minutes

We are given that the distribution of time to complete an exam is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(completing the exam in one hour or less)

P(x < 60)

P( x < 60) = P( z < \displaystyle\frac{60 - 80}{10}) = P(z < -2)

Calculation the value from standard normal z table, we have,  

P(x < 60) =0.023= 2.3\%

b) P(complete the exam in more than 60 minutes but less than 75 minutes)

P(60 \leq x \leq 75) = P(\displaystyle\frac{60 - 80}{10} \leq z \leq \displaystyle\frac{75-80}{10}) = P(-2 \leq z \leq -0.5)\\\\= P(z \leq -0.5) - P(z < -2)\\= 0.309- 0.023 = 0.286= 28.6\%

c) P(completing the exam in more than 90 minutes)

P(x > 90)

P( x > 90) = P( z > \displaystyle\frac{90 -80}{10}) = P(z > 1)

= 1 - P(z \leq 1)

Calculation the value from standard normal z table, we have,  

P(x > 90) = 1 - 0.8413 = 0.1587 = 15.87\%

15.87% of children of class will require more than 90 minutes to complete the test.

Number of children =

\dfrac{15.87}{100}\times 60 = 9.52\approx 10

Approximately, 10 students of class will require more than 90 minutes to complete the test.

You might be interested in
Draw an area model to solve 549÷ 3
Allisa [31]

Answer:

183

Step-by-step explanation:

i cant draw an actual model but 549/3 = 183

7 0
2 years ago
Heellllllllllllllpppppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
iogann1982 [59]

34.76

o

, nearly.

Explanation:

Angle of elevation = arc tan( (vertical height)/(length os the shadow)).

Here, this angle is

arc tan (12.5

/

18) =

34.78

o

, nearly

6 0
3 years ago
Please! Solve f(x)-g(x) if f(x)=1/2x^4 - x^2 and g(x)= 3/4x^4 +3x^3 - x^2
igomit [66]

Answer:

f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}

Step-by-step explanation:

This is a subtraction between polynomials, since both functions are polynomials, hence, to solve the problem with need to perform the subtraction, by coefficients.

f(x)= \frac{1}{2}x^{4}+0x^{3}-x^{2}\\\\g(x)=\frac{3}{4}x^{4}+3x^{3}-x^{2}

By performing the subtraction, we have:

f(x)-g(x)=\frac{-1}{4}x^{4}-3x^{3}

6 0
3 years ago
Check all that apply please
love history [14]

As, synthetic division by -4 gives remainder 0. Hence, Option B is correct. -4 is a root of 3x^{2} +7x-20

As, x+4=0 gives x=-4.

So, option C is correct,

(x+4) is factor of 3x^{2} +7x-20

Option E is correct

\frac{3x^{2} +7x-20 }{x+4}=3x-5

3 0
2 years ago
Earth's radius is approximately 3960 miles. What is the approximate surface area of
den301095 [7]

Answer:

196.9 million mi^2

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Which ordered pair is in Quadrant III?
    6·1 answer
  • Hey can anybody help me with this question please
    5·1 answer
  • What is the discriminant of 9х2 + 2 = 10x?
    7·1 answer
  • What is 7.05 as a mixed number
    14·1 answer
  • For a tile pattern with the rule y = 6x + 4 (where x represents the figure number and y
    10·1 answer
  • Devin has a collection of 40 model vehicles which consists of 25 different cars and 15 different trucks. He selects 8 to display
    12·1 answer
  • Simplify the expression (7 - 2)2 + (6 - 2)3.
    12·2 answers
  • A right angle has a leg of 12 cm and a hypotenuse of 19 cm. What is the length of the other leg?
    10·1 answer
  • HELP I WILL GIVE BRAINLEST, 5 STARS, AND THANKS
    6·2 answers
  • Please please help please please help me please please help
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!