Practice section 1 of 7

Given $X\sim N(50,8)$, find

(i) $P(48<X<54)$,

(ii) $P(X>55)$,

(iii) $P(X<52)$ and

(iv) $P(|X-51|<3)$.

For $X\sim N(2,3)$, find

(i) $P(1.8<X<2.9)$,

(ii) $P(X<2.8)$ and

(iii) $P(|X-2|<2\sqrt 3)$.

If $X\sim N(100,6^2)$, find

(i) $a$ such that $P(X<a)=0.8907$ and

(ii) $b$ such that $P(X>b)=0.770$.

For $X\sim N(60,5^2)$, find

(i) $m$ given $P(X<m)=0.2324$ and

(ii) $n$ given $P(X>n)=0.837$.

If $X\sim N(70,25)$, find $a$ such that $P(|X-70|<a)=0.8$. Hence find the limits containing the central 80% of the distribution.

The heights of male CJCians are normally distributed with mean 169 cm and standard deviation 8 cm. Given that 20% have a height between 160 cm and $d$ cm, with $d>160$, find d. Can we use invNorm(p,μ,σ,CENTER)?