Can someone please help me with math.

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

almond37 [142]

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) Now, here sample of NBA players is 26 so n = 26.

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

6 0

4 years ago

The radius of a circle is 4 inches. What is the circle's circumference?

mojhsa [17]

Answer:

8π inches or approximately 25.12 inches

Step-by-step explanation:

What's the circumference of a circle?

❖ The circumference of a circle is the distance around a circle.

How do we find the circumference of a circle?

❖ The formula to find the circumference of a circle is 2πr, where r =

radius. We can solve in terms of pi, or approximate pi to 3.14

Solving

$\pi * 4*2$
$\pi *8$
8π inches

or

$3.14*4*2$
$3.14*8$
25.12 inches

Have a lovely rest of your day/night, and good luck with your assignments! ♡

7 0

3 years ago

Read 2 more answers

Divide. Write your answer in simplest form. 6/5 divided by 5/8

Anna007 [38]

6/5x8/5

6x8 5x5

48/5x5

48/25

Decimal (1.92)

5 0

3 years ago

Read 2 more answers

Line a and b intersect, forming two adjacent angles, ∠1 and ∠2. If m ∠1= 7x-8 and

german

Answer:

x = 14; y = 8

Step-by-step explanation:

A perpendicular intersection means an intersection between 2 lines, forming angles of 90°. Then:

7x - 8 = 90°

11y + 2 = 90°

7x - 8 = 90

7x = 90 + 8

7x = 98

x = 98/7

x = 14

11y + 2 = 90

11y = 90 - 2

11y = 88

y = 88/11

y = 8

I hope I've helped you.

5 0

3 years ago

Olivia had math and reading homework tonight. Olivia can solve each math problem in 1 minute and she can read each page in 1.5 m

ziro4ka [17]

Answer: the system of equations are

x + y = 22

x + 1.5y = 30

Step-by-step explanation:

Let x represent the number of math problems that Olivia solved.

Let y represent the number of pages that Olivia read.

Olivia completed a total of 22 math problems and pages of reading. This means that

x + y = 22- - - - - - - - - - - - - - -1

Olivia can solve each math problem in 1 minute and she can read each page in 1.5 minutes. Olivia completed a total of 22 math problems and pages of reading in 30 minutes. This means that

x + 1.5y = 30 - -- - - - - - - - - -2

8 0

3 years ago