IB Mathematics Analysis and Approaches 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 $\sigma$.