Question about Binomial distribution

Q) In Joe’s café 70% of customers buy a cup of tea.

In a random sample of 20 customers find the probability that more than 15 buy a cup of tea.

A) Let X the number out of 20 who buy a cup of tea.
X ~ B(20, 0.7)

Since 0.7 is not in the tables, you will need to consider the, complementary random variable Y.

Let Y the number of customers who do not buy a cup of tea.
Y ~ B(20, 0.3)
P(X>15) = P(Y≤4) = 0.2375

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My concern is: We need to find the probability that "more than 15 buy a cup of tea". Because we can't get it directly, so we need to calculate the complementary random variable "Y" first. The final answer, 0.2375, it is the probability that "customers who do not buy a cup of tea", isn't it? Does we need to ues (1-0.2375), to get the probability that "more than 15 buy a cup of tea"???????

Reply 1

joostan

13

Original post by ki_ki_ki

Q) In Joe’s café 70% of customers buy a cup of tea.

In a random sample of 20 customers find the probability that more than 15 buy a cup of tea.

A) Let X the number out of 20 who buy a cup of tea.
X ~ B(20, 0.7)

Since 0.7 is not in the tables, you will need to consider the, complementary random variable Y.

Let Y the number of customers who do not buy a cup of tea.
Y ~ B(20, 0.3)
P(X>15) = P(Y≤4) = 0.2375

---------------------------------------------------------------

My concern is: We need to find the probability that "more than 15 buy a cup of tea". Because we can't get it directly, so we need to calculate the complementary random variable "Y" first. The final answer, 0.2375, it is the probability that "customers who do not buy a cup of tea", isn't it? Does we need to ues (1-0.2375), to get the probability that "more than 15 buy a cup of tea"???????

No, provided your calculations are correct (I've not checked them) there's no need for 1 - 0.2375. Think about it this way, 1 - 0.2375 = 0.7625 It's not possible for the prob of 15 people buying tea to be more than 1 person buying tea. :tongue:

Also my binomial tables have 0.7

(edited 11 years ago)

Reply 2

ki_ki_ki

OP

Original post by joostan

No, provided your calculations are correct (I've not checked them) there's no need for 1 - 0.2375. Think about it this way, 1 - 0.2375 = 0.7625 It's not possible for the prob of 15 people buting tea to be more than 1 person buying tea. :tongue:

Also my binomial tables have 0.7

＂It's not possible for the prob of 15 people buting tea to be more than 1 person buying tea.＂

I'm sorry.... I still can't get it.....

Reply 3

joostan

13

Original post by ki_ki_ki

＂It's not possible for the prob of 15 people buting tea to be more than 1 person buying tea.＂

I'm sorry.... I still can't get it.....

Typo - I meant buying.
P(1 person buys tea) = 0.7 Yes?
P(15 people buy tea) =/= 0.7625 as you suggested, as P(15 people buy tea) < P(1 person buys tea)