Anew catalyst is being investigated for use in the production of a plastic chemical. ten batches of the chemical are produced. the mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. assume the yields are independent and approximately normally distributed. find a 99% confidence interval for the mean yield when the new catalyst is used.

Step-by-step explanation:

Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.

To find : A 99% confidence interval for the mean yield when the new catalyst is used ?

Solution :

Let X be the yield of the batches.

We have given, n=10 , , s=5.8%

Since the size of the sample is small.

We will use the student's t statistic to construct a 995 confidence interval.

From the t-table with 9 degree of freedom for

The 99% confidence interval is given by,

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2