Question

In a taste test of a generic soda versus a brand name soda, 15% of tasters can distinguish between the colas. 45 tasters are asked to take the taste test and guess which cup contains the brand name soda. The tests are done independently in separate locations, so that the tasters do not interact with each other during the test.(a) The count of correct guesses in 50 taste tests has a Binomial distribution. What are n and p? (b) What is the mean number of correct guesses in many repetitions? (c) What is the probability of exactly 8 correct guesses?

Answer 1

Answer: a) n = 50, p = 0.135, b) 6.75, c) 0.134.

Explanation:

Since we have given that

Number of tasters = 45

Percentage of tasters can distinguish between the colas = 15%

Number of taste tests = 50

a) What are n and p?

`n=50\\\\p=((15)/(100)* 45)/(50)\\\\p=(0.15* 45)/(50)\\\\p=0.135`

(b) What is the mean number of correct guesses in many repetitions?

Mean is given by

`np\\\\=50* 0.135\\\\=6.75`

(c) What is the probability of exactly 8 correct guesses?

P(X=8) is given by

`^(50)C_8(0.135)^8(0.865)^(42)\\\\=0.134`

Hence, a) n = 50, p = 0.135, b) 6.75, c) 0.134