Find the indicated probability. Round to the nearest thousandth. A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find
the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
0.985
0.996
0.550
0.143

Step-by-step explanation:

Given

Proportion = 55%

Required

Probability that at least one out of 7 selected finds a job

Let the proportion of students that finds job be represented with p

Convert to decimal

Let the proportion of students that do not find job be represented with q

Such that;

Make q the subject of formula

In probability; opposite probabilities add up to 1;

In this case;

Probability of none getting a job + Probability of at least 1 getting a job = 1

Represent Probability of none getting a job with P(none)

Represent Probability of at least 1 getting a job with P(At least 1)

So;

Solving for the probability of none getting a job using binomial expansion

Where and n = 7; i.e. total number of graduates

For none to get a job, means 0 graduate got a job;

So, we set r to 0 (r = 0)

The probability becomes

Substitute 7 for n

Substitute and

Recall that

Substitute

Make P(At least 1) the subject of formula

(Approximated)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet