Question

The amount of ACME Cola dispensed from the soda fountain each day is known to have a normal distribution with mean 28.7 liters and standard deviation 2.1 liters. In a single day, what is the probability that the amount of soda dispensed is...

1. is within 1.654 liters from the mean and within 1.654 standard deviations from the mean?

Answer 1

Let x be the amount of ACME Cola dispensed from the soda fountain each day.

x follows normal distribution with mean µ = 28.7 and standard deviation σ = 2.1

1) We are asked to find P ( -1.645 < z < 1.645 )

P ( -1.645 < z < 1.645 ) = P( z < 1.645 ) - P( z < -1.645 )

= 0.9500 - 0.05 ---- ( From z score table , table value corresponding to z = 1.645 and z = -1.645 )

= 0.90

Therefore probability that the amount of soda dispensed is within 1.654 standard deviations from the mean is 0.90