Question

The probability of someone buying a particular newspaper in a town is 0.4. Out of 80 customers who come into a shop, what is the probability of at most 26 customers buy this newspaper? Use the normal distribution to approximate the binomial distribution. a) 0.8924 b) 0.1076 c) 0.9550 d) 0.0445

Answer 1

Answer: Therefore, none of the given options (a) 0.8924, b) 0.1076, c) 0.9550, d) 0.0445) is correct. The correct probability is approximately 0.0968.

Explanation:

To find the probability of at most 26 customers buying the newspaper out of 80 customers, we need to use the normal distribution to approximate the binomial distribution.

Given that the probability of someone buying the newspaper is 0.4, we can calculate the mean and standard deviation for the binomial distribution.

Mean (μ) = n * p

μ = 80 * 0.4

μ = 32

Standard Deviation (σ) = √(n * p * q)

σ = √(80 * 0.4 * 0.6)

σ ≈ 4.62

To approximate the binomial distribution using the normal distribution, we can use the continuity correction and calculate the z-score.

Z = (x - μ + 0.5) / σ

Where x is the number of customers (26 in this case)

Z = (26 - 32 + 0.5) / 4.62

Z ≈ -1.30

Using a standard normal distribution table or a calculator, we can find the probability associated with the z-score of -1.30.

The probability of at most 26 customers buying the newspaper is approximately 0.0968.