IB Mathematics Analysis and Approaches Question Type 1: Finding the Number of Standard Deviations a Specific Value Is Away Exercises

Given $X\sim N(\mu ,{\sigma }^2)$ and $P(X>a)=0.34$, find how many standard deviations above the mean $a$ is.

Given a normal random variable $X$ with mean $\mu$ and variance ${\sigma }^2$, if $P(X>a)=0.025$, find $\frac{a-\mu }{\sigma }$.

Let $X\sim N(\mu ,{\sigma }^2)$ and $P(X<a)=0.40$. Calculate the number of standard deviations $a$ is below or above the mean.

Suppose $X\sim N(\mu ,{\sigma }^2)$ and $P(X<a)=0.05$. How many standard deviations below the mean is $a$?

Let $X\sim \text{N}(\mu ,{\sigma }^2)$ and $\text{P}(X>a)=0.005$. Calculate how many standard deviations above the mean $a$ lies.

For $X\sim N(\mu ,{\sigma }^2)$, if $P(X>a)=0.975$, how many standard deviations below the mean is $a$?

Suppose $X\sim N(\mu ,{\sigma }^2)$ and $P(X>a)=0.30$. How many standard deviations above the mean is $a$?

Suppose $X\sim N(\mu ,{\sigma }^2)$ and $P(X>a)=0.1587$. Find $\frac{a-\mu }{\sigma }$.

For a normal distribution $X\sim N(\mu ,{\sigma }^2)$, if $P(X<a)=0.995$, find the number of standard deviations of $a$ above the mean.

For $X\sim N(\mu ,{\sigma }^2)$, if $P(X>a)=0.10$, determine the number of standard deviations that $a$ lies above the mean.

Given a normal variable $X$ with mean $\mu$ and standard deviation $\sigma$, if $P(X<a)=0.8413$, determine the number of standard deviations $a$ is above the mean.

Given $X\sim N(\mu ,{\sigma }^2)$ with $P(X>a)=0.20$, find $\frac{a-\mu }{\sigma }$.