The weight of the eggs produced by a certain breed of hen is normally distributed with mean 65.9 grams (g) and standard deviation 5.5 g. If cartons of such eggs can be considered to be SRSs of size 12 from the population of all eggs, what is the probability that the weight of a carton falls between 775 g and 825 g

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!

y=mx+

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.