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

Answer:

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

Step-by-step 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)  =  $\binom{5}{5}\times 0.35^{5} \times (1-0.35)^{5-5}$

                                  =  $1 \times 0.35^{5} \times 0.65^{0}$

                                  =  0.00525

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