It is estimated that 55% of the freshmen entering a particular college will graduate from that college in four years.

a. For a random sample of 5 entering freshmen, what is the probability that exactly 3 will graduate in four years?

b. For a random sample of 5 entering freshmen, what is the probability that a majority will graduate in four years?

c. 80 entering freshmen are chosen at random. Find the mean and standard deviation of the proportion of these 80 that will graduate in four years.

Step-by-step explanation:

Let x be a random variable representing the number of freshmen that will enter and graduate from the college. This is a binomial distribution since the outcomes are two ways. It is either they graduate or they don't graduate. The probability of success, p = 55/100 = 0.55

The probability of failure, q would be 1 - p = 1 - 0.55 = 0.45

a) We want to determine P(x = 3)

From the binomial distribution table,

P(x = 3) = 0.34

b) A majority would be all 3 and above graduating. From the binomial distribution table,

P(x ≥ 3) = 0.26

c) mean = np

mean = 80 × 0.55 = 44

Standard deviation = √npq

Standard deviation = √80 × 0.55 × 0.45 = 4.45

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺