Question

The weight of crackers in a box is stated to be 16 ounces. The amount that the packaging machine puts in the boxes is believed to have a normal model with mean 16.15 ounces and standard deviation 0.3 ounces.

What is the probability that the weight of a box of crackers is below 16 ounces? Show calculations or TI set up

what is the probability that the mean weight of a 10 box case of crackers is below 16 ounces?

What is the range of the weights for the middle 95% of boxes of crackers?

What is the range of the mean of weights for the middle 95% of 10 box case of crackers?

Answer 1

The Normal Probability Distribution menu for the TI-83+/84+ is found under  DISTR (2nd VARS).

#2: normalcdf
This function returns the cumulative probability from zero up to some input value of the random variable x.

Syntax:  normalcdf (lower bound, upper bound, mean, standard deviation)

normalcdf(-10000,16,16.15,0.3)

P (X<16)=P (Z<−0.5)

=0.3085

b)

middle 95 %

= ( 15.562 , 16.738 )

c)

sd(Xbar) = sd/sqrt(n) = 0.3/sqrt(10) = 0.0948683298

=( 15.964058 ,16.33594 )