Question

Take a spin Refer to Exercise 83. Calculate and interpret $P(X\le 7)$

Short answer

There are $7.26\%$chances that spinner would land in the blue region at most 7 times.

Step-by-step solution

Given Information

Number of trials $\left(n\right)=12$

Probability of success$\left(p\right)=0.80$

Simplification

Consider, $\mathrm{X}$be the random variable that follows the binomial distribution with parameters $n=12$and $p=$$0.80$.

$P(X\le 7)$can be calculated as:

$$\begin{gathered} P(X\le 7)=P(X=0)+P(X=1)+\dots .+P(X=7) \\ =\sum _{r=0}^7{}^{12}C_r\times (0.80{)}^r\times (1-0.80{)}^{12-r} \\ =0.0726 \end{gathered}$$

Hence, the probability is$0.0726$

Interpretation:

There are $7.26\%$chances that spinner would land in the blue region at most 7 times.