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
The area of this square
ANEK [815]

It appears as if 12cm is half the length of the side so we can assume that the total length of one side is 24cm.


The area of a square is given by the equation A=s^{2} where s is the length of the side.  

A=24^{2}

A=576


The area of this square is 576cm2.


Hope this helps!

7 0
3 years ago
Jay gas $8 he wants to buy a book gir $7.50 the sales tax 6% does he have enough money
Reil [10]
6%=0.06
if you want to know how much he paid for the sales taxes you multiply 7.5 by 0.06 
7.5 . 0.06= 0.45
7.5+0.45=7.95
8>7.95
Jay have enough money to buy the book
8 0
3 years ago
Wing Length vs. Age у 18 16 14 12 10 Age 6 ONA O 00 X 5 07 1 2 3 4 Wing Length (in) The y-intercept of the estimated line of bes
kifflom [539]

Answer:

For a glider, which a paper airplane is the more lift the glider has the longer it can fly. However, you must keep the weight and drag in check to avoid flight failure.

Step-by-step explanation:

4 0
3 years ago
(8x² + 3x) - 4x² + x-4
serg [7]

Answer:

4x^2+4x-4

Step-by-step explanation:

8x^2 + 3x - 4x^2 + x - 4

= 8x^2 - 4x^2 + 3x + x - 4

= 4x^2 + 4x - 4

4 0
1 year ago
Math question down below
klio [65]
The dog with the weight of 110lbs is the outlier in the equation--since the other dogs only range from 20 to 35 lbs.
7 0
2 years ago
Read 2 more answers
Other questions:
  • Factor x2 − 4x + 5.<br><br> Prime<br> (x + 5)(x − 1)<br> (x − 5)(x − 1)<br> (x + 5)(x + 1)
    7·1 answer
  • An angle is formed by the union of two _________. rays lines line segments planes
    9·2 answers
  • (x 5 + y 5) divided by (x + y) PLEASE HELP ME!!!
    7·1 answer
  • If 16 counters are 4/9, then what is the ONE?
    8·2 answers
  • suppose that a certain basketball athlete earned $23,000,000 to play 80 games, each last 48 min. how much did the athlete earn p
    13·2 answers
  • Solve the system.
    11·1 answer
  • 4b+3=-9 helppppppppppppppppp
    10·2 answers
  • Identify the terms themselves for the following expression. (separate ur terms with a comma)
    12·2 answers
  • Solve for x.<br> 4(x + 3) = x +42<br> x = [?]
    7·1 answer
  • Which expression is equivalent to the expression shown below?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!