Mathematics, 19.07.2019 01:00 tony7135

If 38% of computer science students in north america last year were women, (a) what is the probability that the top mark was earned by a woman? (b) what is the probability that exactly 6 of the 10 top marks were earned by women? (c) how many women would you expect in the top 10?

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A) The answer is 38%.

The event has only two possible outcomes: the top mark is earned either by a man or by a woman.
The events are also independent of each other: the top mark earner does not depend on who earned the second highest mark.
Therefore, we are talking about a binomial distribution, in which the probability of success (mark earned by a woman) is p(W) = 0.38, which means 38%.

B) The probability that exactly 6 of the 10 top marks were earned by women is 9.34%.

The probability of getting exactly 6 women in 10 marks is given by the formula:
$P(X) = \frac{n!}{k!(n-k)!} p^{k}(1 - p)^{n-k}$

where:
n = total number of events = 10
k = number of success we want = 6
p = probability of a succesfull event = 0.38

Substituting the numbers:
$P(W=6) = \frac{10!}{6!(10-6)!} 0.38^{6}(1 - 0.38)^{10 - 6} \\ 
= \frac{10!}{6!(4)!} 0.38^{6}(0.62)^{4}$

P(W = 6) = 210 · 0.00301 · 0.14776
= 0.0934

Hence, the probability of having 6 women earning among the top 10 marks is 0.0934, which means 9.34%

C) We would expect to have 3 women in the top 10.

We would expect that the percentage of the total population is the same of the top 10 marks, therefore:
W = n · p
= 10 · 0.38
= 3.8

Since we cannot have decimals of a physical person, the closest integer is 3.

Answer from: Quest

use the power rule

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise

to the power of

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in ( x 2 ) 2

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply

2 by 2 . 9 x 4 ( y 3 ) 2

multiply the exponents in

( y 3 ) 2 .

apply the power rule and multiply exponents,

( a m ) n = a m n . 9 x 4 y 3

⋅

multiply

3 by 2 . 9 x 4 y 6

step-by-step explanation:

Answer from: Quest

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

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