Question

The average watermelon weighs 8 lbs with a standard deviation of 1.5. Find the probability that a watermelon will weigh between 6.8 lbs and 9.3 lbs.

Answer 1

Answer:

The  probability that a watermelon will weigh between 6.8 lbs and 9.3 lbs.

P(6.8 ≤X≤9.3) = 0.5932

Step-by-step explanation:

Step 1:-

by using normal distribution find the areas of given x₁ and x₂

Given The average watermelon weighs 8 lbs

μ = 8

standard deviation σ = 1.5

I) when  x₁ = 6.8lbs and  μ = 8 and  σ = 1.5

 $z_{1} = \frac{x_{1} -mean}{S.D} = \frac{6.8-8}{1.5} = - 0.8$

ii)  when x₂ = 9.3 lbs and  μ = 8 and  σ = 1.5

$z_{2} = \frac{x_{2} -mean}{S.D} = \frac{9.3-8}{1.5} = 0.866>0$

Step2:-

The probability that a watermelon will weigh between 6.8 lbs and 9.3 lbs.

P(6.8 ≤X≤9.3) = A(z₂) - A(-z₁)

                      = A(0.866) - A(-0.8)

                       =  A(0.866)+ A(0.8)

check below normal table

                      = 0.3051 + 0.2881

                      = 0.5932

Conclusion:-

The probability that a watermelon will weigh between 6.8 lbs and 9.3 lbs.

P(6.8 ≤X≤9.3) = 0.5932