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
[tex]z_{1} = \frac{x_{1} -mean}{S.D} = \frac{6.8-8}{1.5} = - 0.8<0[/tex]
ii) when x₂ = 9.3 lbs and μ = 8 and σ = 1.5
[tex]z_{2} = \frac{x_{2} -mean}{S.D} = \frac{9.3-8}{1.5} = 0.866>0[/tex]
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
