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Alchen [17]
3 years ago
7

14. Consider the following questions: give the distribution name, carefully define the random variables you use and find the fin

al answer. a) A professor has made 20 exams of which 8 are hard, 7 are reasonable, and 5 are easy. The exams are mixed up and the professor selects 4 of them at random to give to four sections of the course she is teaching. What is the probability that no sections receive a hard test
Mathematics
1 answer:
malfutka [58]3 years ago
6 0

Answer: the probability that no sections receive a hard test is 0.1022

Step-by-step explanation:

Given that;

total number of exams = 20

hard exams = 8

reasonable = 7

easy exam = 5

so total exams that are bot hard = 7 + 5 = 12

we will make use of the probability mass function of hyper geometric distribution;

so the probability that no section of the received a hard test can be determined as follows;

P( x=0; N=20, n=4, k=8 ) = [ ⁸C₀ × ²⁰⁻⁸C₄₋₀ ] / ²⁰C₄

= [1 × ¹²C₄ ] / ²⁰C₄

= [1 × (12!/(4!×(12-4)!) ] / (20!/(4!×(20-4)!)

= [1 × 495 ] / 4845

= 495 / 4845

= 0.1022

Therefore the probability that no sections receive a hard test is 0.1022

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Step-by-step explanation:

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8 0
3 years ago
Which values are solutions to the inequality below? √x &gt; 25?
dezoksy [38]

Answer:

C and D

Step-by-step explanation:

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And since the square root of x is greater than or equal to 25, u can use both of them for answers.

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3 years ago
What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?
Arisa [49]

Answer:

k = 25

Step-by-step explanation:

(2x  - sqrt(k) )^2              Expand this as a binomial                          

4x^2 - 4x*sqrt(k) + k      The middle term must be -20x Solve for k so it is

-4xsqrt(k) = - 20x            Divide by -4x

sqrt(k) = -20x/-4x             Do the division

sqrt(k) = 5                         Square both sides

k = 25


5 0
3 years ago
A number written in expanded form is written has the sum of each blank write 39,005 in expanded form
evablogger [386]
When expanding number, we should separate the numbers according to the places like the number 275 written in expanded form 200+70+5. So, in this question we must likely done like this. The number is 39,005 the sum that is written on expanded form is 30,000+9,000+5.
3 0
3 years ago
Read 2 more answers
Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean valu
Sauron [17]

Answer:

(1) 0.4207

(2) 0.7799

Step-by-step explanation:

Given,

Mean value,

\mu = 15.0

Standard deviation,

\sigma = 1.25

(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)

= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})

=1-P(z\leq \frac{17.5 - 15}{1.25})

=1-P(z\leq \frac{2.5}{1.25})

=1-P(z\leq 2)

=1- 0.5793   ( By using z-score table )

= 0.4207

(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)

=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})

=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})

=P(z\leq 2.4) - P(z\leq -0.8)

= 0.9918 - 0.2119

= 0.7799

8 0
3 years ago
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