Respuesta :
Answer:
Yes, value of adults having exactly 1 credit card is significantly low.
Step-by-step explanation:
We are given that 74% of randomly selected adults have a credit card. Assume that a group of five adults is randomly selected.
And we have to check that if the group of five adults includes exactly 1 with a credit card, is that value of 1 significantly low or not.
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 adults
r = number of success = exactly 1
p = probability of success which in our question is % of adults
having a credit card, i.e; 74%
LET X = Number of adults having a credit card
So, it means X ~ [tex]Binom(n=5, p=0.74)[/tex]
Now, Probability that the group of five adults includes exactly 1 with a credit card is given by = P(X = 1)
P(X = 1) = [tex]\binom{5}{1}\times 0.74^{1}\times (1-0.74)^{5-1}[/tex]
= [tex]5 \times 0.74 \times 0.26^{4}[/tex]
= 0.0169
So, the probability that in a group of five adults, exactly 1 have a credit card is 0.0169 or 1.69%.
Now, for any probability value to be significantly low it must be less than 5% as it is considered very unusual or may be called it that the probability of happening of that event is very rare or low.
Since, here our probability is way less than 5% i.e. 1.69%. So we can conclude that the value of adults having exactly 1 credit card in a group of 5 is significantly very low.
