Question

Assume that the average size for chicken eggs is 49.6 gram with a standard deviation of 7.5 grams. Assume that the egg sizes are normally distributed. a. What is the probability that you will have a size of at least 67.5 gram? b. What is the probability that the average weight of 15 eggs will be between 46 and 51 grams? c. If we call an egg “Peewee” size when it is among the smallest 2 percent of the weight, what is the weight for an egg to be called peewee?

Answer 1

Solution :

Given that ,

mean = = 49.6

standard deviation = = 7.5

a)

P(x 67.5) = 1 - P(x   67.5)

= 1 - P((x - ) / (67.5 - 49.5) / 7.5)

= 1 -  P(z 2.4)  

= 1 - 0.9918 Using standard normal table.   

= 0.0082

Probability = 0.0082

b)

n = 15

= = 49.6

= / n = 7.5 / 15 = 1.9365

P(46 < < 51) = P((46 - 49.5) /1.9365 <( - ) / < (51 - 49.5) / 1.9365))

= P(-1.81 < Z < 0.77)

= P(Z < 0.77) - P(Z <-1.81) Using standard normal table,  

= 0.7794 - 0.0351

= 0.7443

Probability = 0.7443

c)

P( Z < z ) = 2%

P( Z < z ) = 0.02

P( Z < -2.05 ) = 0.02

z = -2.05

Using z - score formula,

X = z * +

= -2.05 * 7.5 + 49.5  

= 31.13