Question

Can you please help me solve these questions on statistics and probability.

Answer 1

Let n = 25, p = 0.4, q = 1-0.4=0.6.

The formula for the binomial probability is as follows:

`P(x)=_nC_xp^x(1-p)^(n-x)`

To obtain the probability of at least 10, solve for P(10)+P(11)+P(12)+...+P(25).

Thus, we have the following.

`\begin{gathered} P(x\ge10)=_(25)C_(10)(0.4)^(10)(0.6)^(25-10)+_(25)C_(11)(0.4)^(11)(0.6)^(25-11)+\cdots+_(25)C_(25)(0.4)^(25)(0.6)^(25-25) \\ =(3268760)(0.4)^(10)(0.6)^(15)+(4457400)(0.4)^(11)(0.6)^(14)+\cdots+(1)(0.4)^(25)(0.6)^0 \\ \approx0.57538298232 \\ \approx0.5754 \end{gathered}`

Therefore, the probability that at least 10 of them prefer the news online is approximately 0.5754 or 57.54%.