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
mash [69]
3 years ago
5

One measure of an athlete’s ability is the height of his or her vertical leap. Many professional basketball players are known fo

r their remarkable vertical leaps, which lead to amazing dunks. DJ Stephens is the current vertical-leap record holder at 46 inches. However, the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.
1. The probability that the mean vertical leap for the 36 players will be less than 26 inches is ________

2. The probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is _______
Mathematics
1 answer:
almond37 [142]3 years ago
6 0

Answer:

(1) P(\bar X < 26 inches) = 0.0436

(2) P(27.5 inches < \bar X < 28.5 inches) = 0.2812

Step-by-step explanation:

We are given that the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

Firstly, Let \bar X = mean vertical leap for the 36 players

Assuming the data follows normal distribution; so the z score probability distribution for sample mean is given by;

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

where, \mu = population mean vertical  leap = 28 inches

            \sigma = standard deviation = 7 inches

            n = sample of NBA player = 36

(1) Probability that the mean vertical leap for the 36 players will be less than 26 inches is given by = P(\bar X < 26 inches)

   P(\bar X < 26) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{26-28}{\frac{7}{\sqrt{36} } } ) = P(Z < -1.71) = 1 - P(Z \leq 1.71)

                                                 = 1 - 0.95637 = 0.0436

(2) <em>Now, here sample of NBA players is 26 so n = 26.</em>

Probability that the mean vertical leap for the 26 players will be between 27.5 and 28.5 inches is given by = P(27.5 inches < \bar X < 28.5 inches) = P(\bar X < 28.5 inches) - P(\bar X \leq 27.5 inches)

    P(\bar X < 28.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{28.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z < 0.36) = 0.64058 {using z table}                      

    P(\bar X \leq 27.5) = P( \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{27.5-28}{\frac{7}{\sqrt{26} } } ) = P(Z \leq -0.36) = 1 - P(Z < 0.36)

                                                        = 1 - 0.64058 = 0.35942

Therefore, P(27.5 inches < \bar X < 28.5 inches) = 0.64058 - 0.35942 = 0.2812

You might be interested in
Pls, help!!!! Will make brainliest!!!
riadik2000 [5.3K]

Answer:

y=2x+6

Step-by-step explanation:

slope intercept formula → y=mx+b

\frac{6-2}{0-(-2)} =\frac{4}{2} =2\\

so 2 is your slope and the point (0,6) crosses the y-intercept at 6 since x = 0

plugin 2 for m (or the slope) and 6 for b (y-intercept)

your answer → y=2x+6

4 0
2 years ago
Sammy is an hourly employee who makes $26 per hour as an elevator technician. He is paid overtime $13 for every hour that he wor
oksian1 [2.3K]

Answer:

364$

Step-by-step explanation:

you multiply 26 times 13 which equals 364

8 0
3 years ago
Linear equations 3(x+1)=3x+3
vaieri [72.5K]
4x + 2 - 3x + 5 - 2(x + 5) = (2x - 5) + (3x + 4) 
4x + 2 - 3x + 5  - 2x - 10 =   2x - 5 +   3x + 4 
4x - 3x - 2x + 5 + 2 - 10  =  2x + 3x - 5 + 4 
        - x             - 3           =       5x       - 1   
-x - 3 = 5x - 1 is the line above recopied 
+x     = +x       
    -3   = 6x - 1 
<span>    +1   =    + 1 </span>
    - 2   = 6x 
    - 2/6 = 6x/6 
    - 1/3 = x, the answer
3 0
3 years ago
a) A six sided dice is unbiased . It is numbered 1,2,3,4,5 and 6 on its faces. The dice is rolled several times until it lands o
masha68 [24]
P(not 5) =5/6 and P(5) = 1/6
If the first 5 is rolled on the 5th roll then the first four rolls were not 5
P(5 on fifth roll) = 5/6 x 5/6 x 5/6 x 5/6 x 1/6 = 5^4/6^5 = 625/7776 = 0.080375...
6 0
1 year ago
Please help me on this and dont play around
katrin [286]

Answer:

ummmm 90% sure its 13/10.......?

Step-by-step explanation:

:/

4 0
3 years ago
Other questions:
  • Angle A is in standard position and terminates in quadrant IV. If sec(A) = 4/3 , complete the steps to find cot(A).  Use the ide
    8·2 answers
  • Jill got an 85% on a math test if there were 40 questions in total,how many did she get wrong?
    11·2 answers
  • How do I find angles a, b, and c?
    15·2 answers
  • If there were 35,000 fatal traffic accidents, how many would be expected to involve drivers in the 55-64 age group?
    15·1 answer
  • In the equation z= x/y – y/x, take x as the numbers given below find number z.
    9·1 answer
  • Please help me with this Algebra question. Who ever gets everything correct will be brainliest!
    13·2 answers
  • Please help,<br> all i have is 16 x 33 = 528cm2 ?!!!
    5·2 answers
  • The ratio of the number of boys to the number of girls in a dance club is 5 : 6. After 6 more boys join the club, the ratio beca
    12·1 answer
  • A diver jumps from a platform diving board that is 32 feet above water. The height , h of the diver above water , in feet, t sec
    8·2 answers
  • en la feria del condado, la calabaza con la cinta roja pesaba 108 libras menos que la calabaza con la cinta azul. cuanto pesaba
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!