Question

) Of the Statistics graduates of a University 35%, received a starting salary of $40,000.00. If 5 of them are randomly selected, find the probability that all the graduated had starting salary of $40,000.00.

Answer 1

The probability that all the graduated had starting salary of $40,000.00 is 0.00525.

Explanation:

We are given that at of the Statistics graduates of a University 35%, received a starting salary of $40,000.00.

Also, 5 of them are randomly selected.

The above situation can be represented through Binomial distribution;

`P(X=r) = \binom{n}{r}p^(r) (1-p)^(n-r) ; x = 0,1,2,3,.....`

where, n = number of trials (samples) taken = 5 graduates

r = number of success = all 5 had starting salary of $40,000

p = probability of success which in our question is % of Statistics

graduates who received a starting salary of $40,000, i.e; 35%

LET X = Number of graduates who received a starting salary of $40,000.00

So, it means X ~ Binom(n = 5, p = 0.35)

Now, Probability that all the graduated had starting salary of $40,000.00 is given by = P(X = 5)

P(X = 5) =
`\binom{5}{5}* 0.35^(5) * (1-0.35)^(5-5)`

=
`1 * 0.35^(5) * 0.65^(0)`

= 0.00525

Hence, the probability that all the graduated had starting salary of $40,000.00 is 0.00525.