Question Type 2: Finding mean and standard deviation given probability and x value Exercises

Let product lifetimes $X \sim N(1000, \sigma^2)$. Given that $P(X < 900) = 0.1587$, find the value of $\sigma$.

The test scores $X$ are normally distributed such that $X \sim N(\mu, 10^2)$. Given that $P(X < 85) = 0.84$, find the value of $\mu$.

If 2.5% of adults exceed 190 cm, find the value of $\sigma$.

Let $X\sim N(\mu,\sigma^2)$. Given $P(X<5)=0.1587$ and $P(X>9)=0.1587$, find $\mu$ and $\sigma$.

Let $X\sim N(\mu,15^2)$. Given $P(X>60)=0.05$, find $\mu$.

Let $X\sim N(100,\sigma^2)$. Given $P(X>120)=0.10$, find the variance of $X$.

Let $X \sim N(80, \sigma^2)$. Given $P(X > 100) = 0.025$, find $\sigma$.

Let $X \sim N(50, \sigma^2)$. Given $P(40 < X < 60) = 0.95$, find $\sigma$.

Let $X \sim N(27, \sigma^2)$. Given $P(X > 32) = 0.16$, find the variance of $X$.

Let $X\sim N(\mu,20^2)$. Given $P(X<150)=0.10$, find $\mu$.

Let measurement errors $X$ be normally distributed such that $X \sim \text{N}(\mu, 25)$. Given $\text{P}(X > 20) = 0.025$, find the value of $\mu$.

Let $X \sim N(40, \sigma^2)$. Given $P(X < 45) = 0.95$, find $\sigma$.