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

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

P(6.8 ≤X≤9.3) = 0.5932

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) = (x_(1) -mean)/(S.D) = (6.8-8)/(1.5) = - 0.8<0`

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

`z_(2) = (x_(2) -mean)/(S.D) = (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