Question

A manufacturing company packages peanuts for Piedmont Airlines. The weights of the individual packages are normally distributed with a mean of 1.4 grams and a standard deviation of 0.6 grams.

What is the probability that your bag of peanuts will weigh:

Less than 1 gram?

Between 1.4 and 1.8 grams?

More than 1 gram?

Answer 1

here we have,

mean = 1.4

standard deviation = 0.6

Z = (X-mean)/standard deviation

a) The probability that your bag of peanuts will weigh Less than 1 gram

P(X<1) =P(Z<(1-1.4)/0.6) =P(Z<-0.6667) = 0.2525

b) The probability that your bag of peanuts will weigh between 1.4 and 1.8 grams

P(1.4<X<1.8) =P((1.4-1.4)/0.6 <X< (1.8-1.4)/0.6) =P(0<X<0.6667) =P(X<0.6667) - P(X<0) =0.7475 - 0.5 =0.2475

c) The probability that your bag of peanuts will weigh more than 1 gram

P(X>1) =P(X>(1-1.4)/0.6) =P(X>-0.6667) =1-P(X<-0.6667) =1-0.2525 =0.7475