Answer:
The probability of the carton weight being between 775g and 825g is 0.71
Step-by-step explanation:
Hello!
The variable of interest is
X: the weight of an egg of a certain breed of hen. (g)
This variable is normally distributed with mean μ= 65.9g and standard deviation σ=5.5 g
If a carton (a random sample of 12 eggs) is taken, you need to calculate the probability of it weighting 775g and 825g, symbolically: P(775≤X[bar]≤825)
For this, you have to use the distribution of the sample mean X[bar]~N(μ;σ²/n)
If the carton weights 775g, then its eggs will have an average weight of 775/12= 64.48g
If the carton weights 825g, then its eggs will have an average weight of 825/12=68.75g
P(64.48≤X[bar]≤68.75)= P(X[bar]≤68.75) - P(X[bar]≤ 64.48)
P(Z≤(68.75-65.5)/(5.5/√12)) - P(Z≤(64.48-65.5)/(5.5/√12))
P(Z≤1.89) - P(Z≤-0.64)= 0.971 - 0.261= 0.71
The probability of the carton weight being between 775g and 825g is 0.71
I hope you have a SUPER day!
