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

Answer:

x = 3.4

Step-by-step 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                                

= > $P(\dfrac{X - \mu }{\sigma } < \dfrac{X - 3.7 }{0.5})=0.25$

= > $P(Z<\dfrac{X - 3.7}{0.5})=0.25$                      

=> $\dfrac{x - 3.7}{0.5}= Z_{0.25}$                

=> $\dfrac{x - 3.7}{0.5}= -0.67$                        

=> x = -0.67 x 0.5 + 3.7                

=> x = 3.365                      

=> x = 3.4