Dean Chalmers and Julian Gilbey Solutions for Chapter: The Normal Distribution, Exercise 7: EXERCISE 8C

If $T~\mathrm{N}\left(10, {\sigma }^2\right)$ and $\mathrm{P}\left(T>14.7\right)=0.04$, find the value of $\sigma$.

(Round answer up to $2$ decimal places)

It is given that $V~\mathrm{N}\left(\mu , 13\right)$ and $\mathrm{P}\left(V<15\right)=0.75$. Find the value of $\mu$.

(Round answer up to $1$ decimal places)

The variable $W~\mathrm{N}\left(\mu ,{\sigma }^2\right)$. Given that $\mu =4\sigma$ and $P(W<83)=0.95$, find the value of $\mu$ and of $\sigma$.

(Write final answer up to $1$ decimal place)

$X$ has a normal distribution in which $\sigma =\mu -30$ and $P(X⩾12)=0.9$. Find the value of $\mu$ and of $\sigma$.

(Write final answer up to $1$ decimal place)

The variable $Q~\mathrm{N}\left(\mu ,{\sigma }^2\right)$. Given that $P(Q<1.288)=0.281$ and $P(Q<6.472)=0.591$ find the value of $\mu$ and of $\sigma$, and calculate $\mathrm{P}\left(4⩽Q<5\right)$.

For the variable $V~\mathrm{N}\left(\mu ,{\sigma }^2\right)$, it is given that $P(V<8.4)=0.7509$ and $P(V>9.2)=0.1385$. Find the value of $\mu$ and of $\sigma$, and calculate $P(V⩽10)$.

(Round answer up to $2$ decimal places)

Find the value of $\mu$ and of $\sigma$ and calculate $P(W>6.48)$ for the variable $W~\mathrm{N}\left(\mu ,{\sigma }^2\right)$, given that $P(W⩾4.75)=0.6858$ and $P(W⩽2.25)=0.0489$.

(Round answer up to $2$ decimal places)

$X$ has a normal distribution, such that $P(X>147.0)=0.0136$ and $P(X⩽59.0)=0.0038$. Use this information to calculate the probability that $80.0⩽X<130.0$.

(Round answer up to $2$ decimal places)