Step by step solution to "According to government data, the probability that an..."

High School
Statistics and Probability
High school statistics
Data distributions

atodion23

Answered question

2021-12-03

According to government data, the probability that an adult was never in a museum is 15%. In a survey of 10 adults, what is the probability that two or fewer were never in a museum?

Answer & Explanation

jackbranv5

Beginner2021-12-04Added 8 answers

Step 1
It is given that

n = 10 and p = 0.15

.
Step 2
The probability mass function of binomial distribution is given below:

P (X = x) =^{n} C_{x} p^{x} {(1 - p)}^{n - x}, x = 0, 1, 2, \dots, n

∴^{n} C_{r} = \frac{n!}{r! (n - r)!}

n \neq n (n - 1) (n - 2) \dots 3 \times 2 \times 1

The required probability is obtained as follows:

P (X \leq 2) = \sum_{x = 0}^{2} \frac{10!}{x! (10 - x)!} {(0.15)}^{x} {(1 - 0.15)}^{10 - x}

= 0.8202

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