Question

The amount of rainfall in January in a certain city is normally distributed with a mean of 3.7 inches and a standard deviation of 0.5 find the value of Q1

Answer 1

x = 3.4

Explanation:

given,

mean = 3.7 inches

standard deviation = 0.5

we want find the value of Q₁ = ?

the value of x such that, P(X < x)= 0.25

= >
`P((X - \mu )/(\sigma ) < (X - 3.7 )/(0.5))=0.25`

= >
`P(Z<(X - 3.7)/(0.5))=0.25`

=>
`(x - 3.7)/(0.5)= Z_(0.25)`

=>
`(x - 3.7)/(0.5)= -0.67`

=> x = -0.67 x 0.5 + 3.7

=> x = 3.365

=> x = 3.4