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
almond37 [142]
3 years ago
8

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association
Mathematics
1 answer:
AlekseyPX3 years ago
8 0

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

<u><em>Let X = time for this event for boys in secondary school</em></u>

SO, X ~ Normal(\mu=460,\sigma^{2} =40^{2})

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

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

where, \mu = mean time = 460 seconds

            \sigma = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

<u>Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;</u>

       P(X > x) = 0.10   {where x is the required time which boy need to beat}

       P( \frac{X-\mu}{\sigma} > \frac{x-460}{40} ) = 0.10

        P(Z > \frac{x-460}{40} ) = 0.10

<em>So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;</em>

<em>                   </em>      \frac{x-460}{40} =1.2816

                         {x-460}{} =1.2816\times 40

<em>                           </em>x = 460 + 51.264 = <u>511.264 seconds</u>

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

You might be interested in
The sum of two numbers is -9. The difference of the two numbers is -41. What are the two numbers?
Nataly [62]

Answer:

the two numbers are 16 and -25

Step-by-step explanation:

Let the two numbers be x and y

x+y=-9

x-y=-41

By substitution

y=-9-x

x-(-9-x)=-41

x+9+x=-41

2x=-41-9

2x=-50

x=-25

y=-9-(-25)

y=16

6 0
3 years ago
On a standard circular 12-hour clock, the numerals 12 and 6 are opposite each other. On the planet Bajor, they use a circular te
anastassius [24]
Opposite Numbers and their Sums:

1+6=7
2+7=9
3+8=11
4+9=13
5+10=15

Because of this, the pair of opposite numbers are 3 and 8 if you want the pair that equal 11.
7 0
3 years ago
Arrange the expressions in increasing order of their values.
iren [92.7K]

Answer:

The 4th one is the least so you would put that as the first one, then the 2nd one, then the 1st one, then the 3rd one.

Step-by-step explanation:

The fourth one is first because 10 to the power of 0 is 0 times 10 to the power of 1 is still 0 minus 1 to the power of 10 is 1 so 0 minus 1 is -1. The second one is second because 10 to the power of 0 times 10 to the power of 1 is 0, times 1 to the power of 10 is still 0. The first one is third in line because 10 to the power of 0 plus 10 to the power of 1 is 10 times 1 to the power of 10 is 10. The third one is last because its the greatist, 10 to the power of 0 plus 10 to the power of 1 is 10 plus 1 to the power of 10 is 11.

7 0
2 years ago
Glen, Andre, and Ramón share the cost of renting a vacation cottage. The total cost is $960. Glen pays 30% of the total cost. An
SashulF [63]

Answer:

Ramon pays $240.

Step-by-step explanation:

30% of $960 is $288, so Glen pays $288

0.45 = 45%

45% of $960 is $432, so Andre pays $432

30% + 45% = 75% meaning Ramon pays 100% - 75% which is 25%.

25% of $960 is $240. So, Ramon pays $240.

You could also add up the payments of Andre and Glen and subtract that sum from $960 to get the same answer.

8 0
3 years ago
Solve for x: 2sin^2(x) -sin(x)=1 over the interval 0 to 2pi
Zepler [3.9K]
2\sin^2x-\sin x=1\ \ \ \ |subtract\ 1\ from\ both\ sides\\\\2\sin^2x-\sin x-1=0\ \  \ \ |subtitute\ \sin x=t\ where\ t\in[-1;\ 1]\\\\2t^2-t-1=0\\\\2t^2-2t+t-1=0\\\\2t(t-1)+1(t-1)=0\\\\(t-1)(2t+1)=0\iff t-1=0\ or\ 2t+1=0\\\\t=1\ or\ 2t=-1\to t=-\dfrac{1}{2}\\\\therefore\\\sin x=1\ or\ \sin x=-\dfrac{1}{2}\\\\Answer:\boxed{t\in\left\{\dfrac{\pi}{2};\ \dfrac{7\pi}{6};\ \dfrac{11\pi}{6}\right\}}
6 0
3 years ago
Other questions:
  • Five times the sum of a number (x) and three is equal to the sum of that number (x) and fifteen.
    12·2 answers
  • A cone is not a polyhedron. true or false?
    15·2 answers
  • Is there a solution <br> y=3x+1 y=3x+5
    12·2 answers
  • Taylor scored a total of 168 points in basketball this season. He scored 147 of those points in the regular season and the rest
    8·1 answer
  • The table contains data on the number of people visiting a historical landmark over a period of one week. Which type of function
    10·2 answers
  • 8 k+d use k=2 and d=3​
    6·1 answer
  • Pete bought a 5-ounce box of cereal for $5.45. What was the cost per ounce?
    13·2 answers
  • Find the slope of the line through the pair of points: (5, 20) and (4, -17)
    8·2 answers
  • What number could make this equations have no value of x. 3x+8 = 3x + ?
    14·2 answers
  • Ronald is making hats and scarves for charity. He has enough yarn to make 5 hats and 8 scarves. Takes him 12 hrs to knit a hat,
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!