chapter 3 - 4 practice test\ndue sun sep 23, 2025 11:59pm\nattempt 1\nin progress\nnext up: submit…

Explanation:

Step1: Calculate the mean ($\mu$)

The formula for the mean of a discrete - random variable is $\mu=\sum_{i}x_ip_i$. $\mu=(10\times0.09)+(11\times0.12)+(12\times0.51)+(13\times0.14)+(17\times0.14)$ $=0.9 + 1.32+6.12 + 1.82+2.38$ $=12.54$

Step2: Calculate the variance ($\sigma^{2}$)

The formula for the variance is $\sigma^{2}=\sum_{i}(x_i - \mu)^2p_i$. $(10 - 12.54)^2\times0.09+(11 - 12.54)^2\times0.12+(12 - 12.54)^2\times0.51+(13 - 12.54)^2\times0.14+(17 - 12.54)^2\times0.14$ $=(- 2.54)^2\times0.09+(-1.54)^2\times0.12+(-0.54)^2\times0.51+(0.46)^2\times0.14+(4.46)^2\times0.14$ $=6.4516\times0.09 + 2.3716\times0.12+0.2916\times0.51 + 0.2116\times0.14+19.8916\times0.14$ $=0.580644+0.284592 + 0.148716+0.029624+2.784824$ $=3.8284$

Step3: Calculate the standard deviation ($\sigma$)

The standard deviation is the square - root of the variance. $\sigma=\sqrt{\sigma^{2}}$. $\sigma=\sqrt{3.8284}\approx1.9566$

Answer:

Mean: $12.54$ Variance: $3.8284$ Standard Deviation: $1.9566$ Expected Value (same as mean for discrete random variable): $12.54$