Question

According to government​ data, the probability that an adult was never in a museum is 10​%. In a random survey of 60 ​adults, what is the mean and standard deviation of the number that were never in a​ museum? Round to the nearest thousandth.

Answer 1

`\text{Mean}=)=6\\\\\text{Standard deviation}=2.324`

Explanation:

Given : The probability that an adult was never in a museum is : p=0.10

The number of adults randomly surveyed: n = 60

In Binomial distribution , the formula to find the mean and the standard deviation is given by :-

`\text{Mean}=np\\\\\text{Standard deviation}=√(np(1-p))`

Then , the mean and standard deviation of the number that were never in a​ museum will be :-

`\text{Mean}=60(0.10)=6\\\\\text{Standard deviation}=√(60(0.10)(1-0.1))=2.3237900077\approx2.324`