Question

Assume that 74% of randomly selected adults have a credit card. Assume that a group of five adults is randomly selected. If the group of five adults includes exactly 1 with a credit card, is that value of 1 significantly low

Answer 1

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;

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

where, n = number of trials (samples) taken = 5 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 ~ $Binom(n=5, p=0.74)$

Now, Probability that the group of five adults includes exactly 1 with a credit card is given by = P(X = 1)

                 P(X = 1)  = $\binom{5}{1}\times 0.74^{1}\times (1-0.74)^{5-1}$

                               = $5 \times 0.74 \times 0.26^{4}$

                               = 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.