Question

The distribution of the weights ofloaves of bread from a certain bakery follow approximately a normaldistribution. Based on a very large sample, it was found that 10percent of the loaves weighed less than 15.34 ounces, and 20percent of the loaves weighed more than 16.31 ounces. What are themean and standard deviation of the distribution of the weights ofthe loaves of bread?

A. μ = 15.82, σ =.48
B. μ = 15.82, σ =.69
C. μ = 15.87, σ =.50
D. μ = 15.93, σ =.46
E. μ = 16.00, σ =.50

Answer 1

D)

Explanation:

ASSUMING NORMAL DISTRIBUTION, LESS THAN 10% AT LOWER END

OF 15.34 MEANS [DENOTING MEAN BY M AND Standard Deviation. BY S]

M±AS=20%....................M-AS=15.34

FOR 20% LEVEL .......A=1.281........FROM TABLES

M-1.281×S=15.34............................1

SIMILARLY

M±BS=40%...................M+BS=16.31

FOR 40% LEVEL .............B=0.841...................FROM TABLES

M+0.841×S=16.31.............................2

EQN.2 - EQN.1

2.122×S=0.97

S=0.457=0.46

M=15.926= 15.93

HENCE, D IS THE ANSWER

that is D. μ = 15.93, σ =.46