Aparticular concentration of a chemical found in polluted water has been found to be lethal to 40% of the crayfish that are exposed to the concentration for 24 hours. 22 crayfish are placed in a tank containing this concentration of chemical in the water.
(a) what is the probability that 13 or 17 survive?
(b) what is the probability that at least 17 survive?
(c) what is the probability that at most 16 survive?
(d) what number of crayfish are expected to survive?
(e) what is the variance in the number of crayfish that are expected to survive? no actual crayfish were harmed in the making of this question.

a)

b)

c)

d)

e)

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

3) Part a

4) Part b

5) Part c

6) Part d

The expected value is:

7) Part e

The variance is given by:

i need more info. are you looked to see there mph? how much they deliver? how far they go?

step-by-step explanation:

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.