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3 years ago

A basketball player has made 6060% of his foul shots during the season. Assume the shots are independent.

Mathematics

1 answer:

motikmotik3 years ago

7 0

Answer:

a) 2.5 shots

b) 59.4 shots

c) 4.87 shots

Step-by-step explanation:

Probability of making the shot = 0.6

Probability of missing the shot = 0.4

a) The expected number of shots until the player misses is given by:

$E(X) = \frac{1}{P(X)}=\frac{1}{0.4} \\E(X) = 2.5\ shots$

The expected number of shots until the first miss is 2.5

b) The expected number of shots made in 99 attempts is:

$E=99*0.6\\E=59.4\ shots$

He is expected to make 59.4 shots

c) Let "p" be the proportion shots that the player make, the standard deviation for n = 99 shots is:

$s=\sqrt{n*p*(1-p)}\\ s= 4.87\ shots$

The standard deviation is 4.87 shots.

You might be interested in

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with me

inn [45]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

Mean (m) = 266 days

Standard deviation (s) = 16 days

A.) p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = - 1.96 (Z probability calculator)

x - 266 = - 31.36

x = - 31.36 + 266

x = 234.64

B.)

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = - 1.96 (Z probability calculator)

x - 266 = - 31.36

x = - 31.36 + 266

x = 234.64

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = 1.96 (Z probability calculator)

x - 266 = 31.36

x = 31.36 + 266

x = 297.36

Hence,

234.64 < x <297.36

C.)

p(( Z ≤ (x - m) /s) = 2.5%

p(( Z ≤ (x - 266) /16) = 0.025

(x - 266) /16 = 1.96 (Z probability calculator)

x - 266 = 31.36

x = 31.36 + 266

x = 297.36

4 0

2 years ago

Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :