Which names the figure correctly?

A national college researcher reported that 65% of students who graduated from high school in 2012 enrolled in college. Twenty n

Usimov [2.4K]

Answer:

a) The probability that exactly 17 of them enroll in college is 0.116.

b) The probability that more than 14 enroll in college is 0.995.

c) The probability that fewer than 11 enroll in college is 0.001.

d) It would be be unusual if more than 24 of them enroll in college since the probability is 0.009.

Step-by-step explanation:

We can model this with a binomial distribution, with n=29 and p=0.65.

The probability that k students from the sample who graduated from high school in 2012 enrolled in college is:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{29}{k} 0.65^{k} 0.35^{29-k}\\\\\\$

a) The probability that exactly 17 of them enroll in college is:

$P(x=17) = \dbinom{29}{17} p^{17}(1-p)^{12}=51895935*0.0007*0=0.116\\\\\\$

b) The probability that more than 14 of them enroll in college is:

$P(X>14)=\sum_{15}^{29} P(X=k_i)=1-\sum_{0}^{14} P(X=k_i)\\\\\\P(x=0)=0\\\\P(x=1)=0\\\\P(x=2)=0\\\\P(x=3)=0\\\\P(x=4)=0\\\\P(x=5)=0\\\\P(x=6)=0\\\\P(x=7)=0\\\\P(x=8)=0\\\\P(x=9)=0\\\\P(x=10)=0.001\\\\P(x=11)=0.002\\\\P(x=12)=0.005\\\\P(x=13)=0.013\\\\P(x=14)=0.027\\\\\\P(X>14)=1-0.005=0.995$

c) Using the probabilities calculated in the point b, we have:

$P(X$

d) The probabilities that more than 24 enroll in college is:

$P(X>24)=\sum_{25}^{29}P(X=k_i)\\\\\\ P(x=25) = \dbinom{29}{25} p^{25}(1-p)^{4}=23751*0*0.015=0.007\\\\\\P(x=26) = \dbinom{29}{26} p^{26}(1-p)^{3}=3654*0*0.043=0.002\\\\\\P(x=27) = \dbinom{29}{27} p^{27}(1-p)^{2}=406*0*0.123=0\\\\\\P(x=28) = \dbinom{29}{28} p^{28}(1-p)^{1}=29*0*0.35=0\\\\\\P(x=29) = \dbinom{29}{29} p^{29}(1-p)^{0}=1*0*1=0\\\\\\\\P(X>24)=0.007+0.002+0+0+0=0.009$

6 0

3 years ago

Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither. 5x/ x3 + 5x2 + 6x

tatiyna

Answer: hole at x = 0, asymptotes at x = -2 and x = -3

<u>Step-by-step explanation:</u>

$\frac{5x}{x^{3} + 5x^{2} + 6x}$

= $\frac{5x}{x(x^{2}+5x + 6)}$

= $\frac{5x}{x(x+2)(x+3)}$

x ≠ 0 ---> the x cancels out so this is a hole

x + 2 ≠ 0 ---> x ≠ -2 ---> asymptote at x = -2

x + 3 ≠ 0 ---> x ≠ -3 ---> asymptote at x = -3

3 0

3 years ago

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Please show your work how you solved this ! Please answer this !!

ValentinkaMS [17]

Answer:

-5xa^2-7a^3+7a^2+4

Step-by-step explanation:

6 0

3 years ago

Is it ever possible that cos (A−B)=cos ⁡A−cos ⁡B? Why

svetlana [45]

Answer:

yes, there are an infinite number of solutions

Step-by-step explanation:

The attached graph shows values of A and B (x and y) that can make this equation be true. Any of the points on any of the curves will satisfy the equation. (The repetition continues indefinitely in all directions.)

8 0

3 years ago

PLSS HELP IF YOU TURLY KNOW THISS

vredina [299]

Answer:

3

Step-by-step explanation:

8x-4=20

+4. +4

8x=24

8. 8

x=3

6 0

3 years ago

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