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 buying this newspaper?

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.

Step-by-step 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.

Answer 2

To find the probability of at most 26 customers buying this particular newspaper, we need to calculate the cumulative probability up to 26 customers. This can be done using the binomial probability formula.

Step-by-step explanation:

To find the probability of at most 26 customers buying this particular newspaper, we need to calculate the cumulative probability up to 26 customers. This can be done using the binomial probability formula.

The binomial probability formula is:

P(X ≤ r) = Σ(i=0 to r) [nCr * p^i * (1-p)^(n-i)]

In this case, n = 80 (total number of customers), r = 26 (maximum customers buying the newspaper), and p = 0.4 (probability of a customer buying the newspaper).

Using this formula, we can calculate the probability of at most 26 customers buying the newspaper.