Based on data a coffee shop owner has collected,

Ответ:

davisz23

23.01.2022

Probability that no more than 2 of these last 6 customers will want a cookie is 0.974.

Step-by-step explanation:

We are given that Based on data a coffee shop owner has collected, she believes that 12% of her customers will buy a cookie to go with their coffee and that these purchases are independent.

One day as she’s getting ready to close, 6 customers enter the shop and she has only 2 cookies left.

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 = 6 customers

r = number of success = no more than 2

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

customers who will buy a cookie, i.e; 12%

LET X = Number of customers who will want a cookie

So, it means X ~ Binom( n=6, p=0.12 )

Now, probability that no more than 2 of these last 6 customers will want a cookie is given by = P(X $\leq$ 2)

P(X $\leq$ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{6}{0}\times 0.12^{0} \times (1-0.12)^{6-0}+ \binom{6}{1}\times 0.12^{1} \times (1-0.12)^{6-1}+ \binom{6}{2}\times 0.12^{2} \times (1-0.12)^{6-2}$

= $1 \times 1 \times 0.88^{6} +6 \times 0.12 \times 0.88^{5} +15 \times 0.12^{2} \times 0.88^{4}$

= 0.974

Hence, the probability that no more than 2 of these last 6 customers will want a cookie is 0.974.

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