Answer to Question #210334 in Statistics and Probability for saria

Question

The weights of normally distributed withe mean μ mg and standard deviation with σ mg. It is known that 25% of apples are heavier than 172 mg and 10% are lighter than 150 mg.

i) iilustrate the diagram to show the distribution of weghts based on the given information μ=150+1.2801σ

Answer 1

(a).

$P\left(X<150\right)=0.10$

$P\left[\frac{\left(X-\mu \right)}{\sigma }<\frac{\left(150-\mu \right)}{\sigma }\right]=0.10\:\:$

$P\left[Z<\frac{\left(150-\mu \right)}{\sigma }\right]$

From Z - tables, we get:

$P\left(Z<-1.281\right)=0.10$

$-1.281=\frac{\left(150-\mu \right)}{\sigma }$

$\mu =150+1.281\sigma$