The probability that a vehicle will change lanes while making a turn is 45%. Suppose a random sample of 7 vehicles are observed making turns at a busy intersection. Find the probability that a least 5 vehicles will change lanes while making the turn.

Using the binomial distribution, it is found that there is a 0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.

For each vehicle, there are only two possible outcomes, either they change lanes while making a turn, or they do not. The probability of a vehicle changing lanes while making a turn is independent of any other vehicle, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

In this problem:

The probability that at least 5 vehicles will change lanes while making the turn is:

In which

Then

0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.

To learn more about the binomial distribution, you can take a look at link

0.1529

Step-by-step explanation:

Given that:

Probability of changing lane ; p = 45% = 0.45

Sample size (number of trials) = n = 7

Probability that atleast 5 vehicles will change lane :

Using the binomial probability formula :

P(x = x) = nCx * p^x * (1 - p)^(n-x)

(1 - p) = 1 - 0.45 = 0.55

P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)

P(x = 5) = 7C5 * 0.45^5 * 0.55^2

P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221

P(x = 6) = 7C6 * 0.45^6 * 0.55^1

P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969

P(x = 7) = 7C7 * 0.45^7 * 0.55^0

P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736

P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)

P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736

P(x ≥ 5) = 0.152926

P(x ≥ 5) = 0.1529

1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz

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.