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The mailing list of an agency that markets scuba-diving trips to the Florida Keys contains 78% males and 22% females. The agency

choli [55]

Answer:

a) 0.98% probability that 17 of the 29 people are men.

b) 3.86% probability that the first woman is reached on the 8th call

Step-by-step explanation:

For each person chosen by the agency, there are only two possible outcomes. Either it is a man, or it is a woman. The probability of selecting a man or a women in each trial is independent from other trials. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

(a) What is the probability that 17 of the 29 people are men?

This is P(X = 17) when $n = 29, p = 0.78$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 17) = C_{29,17}.(0.78)^{17}.(0.22)^{12} = 0.0098$

0.98% probability that 17 of the 29 people are men.

(b) What is the probability that the first woman is reached on the 8th call?

On the first 7 trials, all men, each with a 78% probability.

On the 8th trial, a women, with a 22% probability. So

$P = (0.78)^{7}*0.22 = 0.0386$

3.86% probability that the first woman is reached on the 8th call

4 0

3 years ago

Simplify square root of 2 over cube root of 2.

Fed [463]

Answer:

2 to the power of one sixth

Step-by-step explanation:

Assuming you don't already know this, any type of root can be expressed as an exponent. Generally speaking:

$\sqrt[n]{x} = {x}^{ \frac{1}{n} }$

So you can rewrite the given fraction as

$\frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{3} } }$

and then reduce as you normally would. That is, if the bases of the numerator and denominator are the same, then you can subtract the denominator's exponent from the numerator's exponent like so:

$\frac{ {2}^{ \frac{1}{2} } }{ {2}^{ \frac{1}{3} } } = {2}^{ \frac{1}{2} - \frac{1}{3} }$

Since

$\frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{1}{6}$

the answer is

${2}^{ \frac{1}{6} } \: or \: \sqrt[6]{2}$

3 0

3 years ago

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Will a geometric figure and its rotated image always,sometimes,or never have to same perimeter?

mash [69]

They will have the same Perimeter, unless you shrink or grow the image then nothing with change

7 0

3 years ago

Please please help me out

masya89 [10]

Answer: y = 3x + 1

Step-by-step explanation:

The equation is in Slope-Intercept format: y = mx + b where

m is the slope (difference in y's over difference in x's)
b is the y-intercept (value of y when x = 0)

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\\text{Let }(x_1,y_1)=(0,1)\quad \text{and}\quad \text{let }(x_2, y_2)=(1,4)\quad then\\\\m=\dfrac{4-1}{1-0}=\dfrac{3}{1}=3$

b = 1 refer to the table that shows y = 1 when x = 0

Now input m = 3 and b = 1 into the Slope-Intercept formula:

y = 3x + 1

8 0

2 years ago

8,264 is divisible by 3? True or false?

mars1129 [50]

$Number\ is\ divisible\ by\ 3\ if\ the\ sum\ of\ the\ digits\ is\ divisible\ by\ 3.\\\\8,264\\\\8+2+6+4=20-
is\ not\ divisible\ by\ 3.\\\\8,264\ is\ divisible\ by\ 3-FALSE$

7 0

3 years ago

Read 2 more answers