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
Semenov [28]
3 years ago
6

The distances male long jumpers for State College jump are approximately normal with a mean of 263 inches and a standard deviati

on of 14 inches. Suppose a male long jumper's jump is ranked in the 75th percentile. How long was his jump?
Mathematics
2 answers:
Effectus [21]3 years ago
7 0

Answer:

His jump was of 272.45 inches

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 263, \sigma = 14

75th percentile

X when Z has a pvalue of 0.75. So X when Z = 0.675

Z = \frac{X - \mu}{\sigma}

0.675 = \frac{X - 263}{14}

X - 263 = 14*0.675

X = 272.45

His jump was of 272.45 inches

kaheart [24]3 years ago
7 0

Answer:

z=0.674

And if we solve for a we got

a=263 +0.674*14=272.436

So the value of height that separates the bottom 75% of data from the top 25% is 272.436.  

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 distances of a population, and for this case we know the distribution for X is given by:

X \sim N(263,14)  

Where \mu=263 and \sigma=14

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=263 +0.674*14=272.436

So the value of height that separates the bottom 75% of data from the top 25% is 272.436.  

You might be interested in
Complete the following invoice for upholstery fabric.
Degger [83]

Answer:

a) $49.48

b) $220921.91

Step-by-step explanation:

(a) 4 yd @ $12.37 per yd = 4 x $12.37 = $49.48

(b) 271 yd @ 815.21 per yd = 271 x $815.21 = $220921.91

(c) 20% yd @ $4.95 per yd : Here the nunber of yards are missing. Hence could not be answer . However if number of yards is x . The answer would be

20% of 4.95x

(20%=0.20)

0.20 × 4.95x

8 0
3 years ago
A right rectangular prism has a length of 9, a width of 4, and a height of 5. How many unit cubes can fit in the prism?
Serjik [45]

Answer:

The answer is 54 cubes.

Step-by-step explanation:

5 0
3 years ago
If you answer I will mark you Brainliest!
Olin [163]

Answer:

divide the figure into two parts.

area of triangle = 1/2×base×height

area of triangle = 1/2×3×3

area pf triangle = 4.5 units²

area of square = side²

area of square = 3²

area of square = 9unit²

5 0
2 years ago
Read 2 more answers
Help plzzzz and tysm &lt;3. I love you all but plz do this asap! Thank you like againnn, take you’re time!
malfutka [58]

Answer:

1.12+36=48.

2)125-25=100

3)5+100=105

4)64-30=34

7 0
3 years ago
Read 2 more answers
1. The diameter of a sphere is 21.6 cm. The volume of the sphere is __
sveta [45]
Detailed Answers:

Volume of a Sphere (V) = 4/3 πr^3

1. Diameter (d) = 21.6 cm
Radius (r) = 21.6/2 = 10.8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (10.8)^3
= 4/3 * 22/7 * 1259.712
= 88/21 * 1259.712
=> 5278.79

Volume (V) = 5278.79 cm^3

2. Diameter (d) = 16 cm
Radius (r) = 16/2 = 8 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (8)^3
= 4/3 * 22/7 * 512
= 88/21 * 512
=> 2145.52

Volume (V) = 2145.52 cm^3

3. Diameter (d) = 24 cm
Radius (r) = 24/2 = 12 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (12)^3
= 4/3 * 22/7 * 1728
= 88/21 * 1728
=> 7241.14

Volume (V) = 7241.14 cm^3

4. Diameter (d) = 6 cm
Radius (r) = 6/2 = 3 cm

Therefore,
= 4/3 πr^3
= 4/3 * 22/7 * (3)^3
= 4/3 * 22/7 * 27
= 88/21 * 27
=> 113.14

Volume (V) = 113.14 cm^3
6 0
1 year ago
Read 2 more answers
Other questions:
  • Find an equation of the sphere with center (4, −12, 8) and radius 10. use an equation to describe its intersection with each of
    13·1 answer
  • 2+0=2 What property is illustrated? A. associative property of addition B. commutative property of addition C. identity property
    7·2 answers
  • ms turner drove 825 miles in march. she drove 3 times as many miles i march as she did in january.she drove 4 times as many mile
    10·1 answer
  • 256 miles per 8 gallons
    15·1 answer
  • An equation for the line that has a slope of 1/2 and passes through the point (-2,5)
    9·1 answer
  • An airplane reaches a maximum height of 34,320 feet. there are 5,280 feet in 1 mile. what is the maximum height, in miles, this
    11·1 answer
  • Which expression is equivalent to t + 4 + 3 - 2t<br><br> 1. t+7<br> 2. -t+7<br> 3. 6t<br> 4. 10t
    13·1 answer
  • Four friends were born in consecutive years. The sum of their
    7·1 answer
  • Find the slope of the line that passes through the points (4, 3) and (2, 7).
    6·1 answer
  • Which polynomial is prime?<br> Ox+3x²-x²-3<br> Ox4-3x²-x² + 3<br> O 3x²+x-6x-2<br> O 3x²+x-6x + 3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!