Respuesta :
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;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
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) = [tex]\binom{5}{5}\times 0.35^{5} \times (1-0.35)^{5-5}[/tex]
= [tex]1 \times 0.35^{5} \times 0.65^{0}[/tex]
= 0.00525
Hence, the probability that all the graduated had starting salary of $40,000.00 is 0.00525.
