Topic 4.12: Standardized Normal and Inverse Questions

X ~ N(50, 6²). Find the z-value of x = 62.

X ~ N(25, 4²). A value has a z-value of 1.75. Find x.

$X\sim N(150,20^2)$ models the mass in grams of a loaf. Find the value $x$ with $P(X<x)=0.9$.

$X\sim N(80,12^2)$. Find the z-value of $x=62$.

Explain what it means for a data value to have a z-value of 0.

X ~ N(200, 25²). Find the value x such that P(X < x) = 0.85.

X ~ N(80, 12²). Find the z-value of x = 62.

$X\sim N(50,6^2)$. Find the z-value of $x=62$.

$X\sim N(25,4^2)$. A value has a z-value of 1.75. Find x.

$X\sim N(200,25^2)$. Find the value x such that $P(X<x)=0.85$.

The journey times of a bus route are normally distributed with mean μ minutes and standard deviation σ minutes.

The probability that a value chosen at random is less than 40 minutes is 0.69146. The probability that it lies between 40 minutes and 50 minutes is 0.30719.

Find the value of μ and the value of σ.

$X\sim N(60,8^2)$. Find x such that $P(X>x)=0.1$.

Exam marks are $X\sim N(58,12^2)$. The top 15% receive a distinction. Find the minimum mark for a distinction.

A value in $X\sim N(40,{\sigma }^2)$ has $z=2.5$ and equals 55. Find σ.

In Maths (mean 65, sd 10) a student scores 80; in Physics (mean 70, sd 5) they score 79. In which subject did they do better relative to the class?

A normally distributed value has z = −1.2, mean 100 and standard deviation 15. Find the value x.

X ~ N(60, 8²). Find x such that P(X > x) = 0.1.

A normally distributed value has $z=-1.2$, mean 100 and standard deviation 15. Find the value x.

$X\sim N(40,5^2)$. Find the two values between which the central 90% of the data lies.

Lifetimes are $X\sim N(600,{\sigma }^2)$ hours, and 20% last less than 540 hours. Find $\sigma$.