Answer:
83.85% of the population is between 46.5g and 65.7g
Explanation:
the 68-95-99.7 rule states that the probability that a random variable (X=Weights of the eggs) is found inside 1 standard deviation , 2 standard deviations and 3 standard deviations from the mean is 68% , 95% , 99.7% respectively
then calling Z to
Z= (X-μ)/σ
where μ= mean , σ = standard deviation , then
for X₁=46.5g
Z₁= (X₁-μ)/σ = (46.5g - 51.3g)/4.8 g= -1
1 standard deviation from both sides (±1) = 68%
then since the normal distribution is symmetrical
1 standard deviation from one side (±1) = 68%/2 = 34%
for X₂=46.5g
Z₂= (X₂-μ)/σ = (65.7 g - 51.3g)/4.8 g= +3
3 standard deviation from both sides (±1) = 99.7%
then since the normal distribution is symmetrical
3 standard deviation from one side (±1) = 99.7%/2 = 49.85%
then
between -1 standard deviation from the mean and +3 standard deviations from the mean there is= 34% + 49.85% = 83.85% of the population (since the regions do not overlap each other)
