Answer to Question #194495 in Statistics and Probability for Daniela(me)

Question

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14. Weights of a certain model of fully loaded gravel trucks follow a normal distribution with mean 

 = 6.4 tons and standard deviation  = 0.4 ton.

 

a) For a truck selected at random, what is the 

probability the weight will be 

less than 5.9 tons?

 

 

 

 

b) For a truck selected at random, what is the 

probability the weight will be 

more than 7 tons?

 

 

 

 

 

c) For a truck selected at random, what is the 

probability the weight will be 

between 5.4 and 6.4 tons?

 

 

 

Answer 1

We have given that,

$\mu = 6.4$

$\sigma = 0.4$

a.) The probability the weight will be less than 5.9 tons

$=P(X<5.9)$

$=P(Z<\dfrac{5.9-6.4}{0.4})$

$=P(Z<-1.25) = 0.10$

b.) The probability the weight will be more than 7 tons

$=P(X>7)$

$=P(Z>\dfrac{7-6.4}{0.4})$

$=P(Z>1.5)$

$=0.10$

c.) The probability the weight will be between 5.4 and 6.4 tons

$P(5.4<X<6.4)$

$= P(\dfrac{5.4-6.4}{0.4}<Z<\dfrac{6.4-6.4}{0.4})$

$= P(-2.5<Z<0)$

$= 0.49$