Statistics
posted by Lexi on .
I have 2 statistics problems that I've done and felt completely confident with them until I worked the problem a different way and got a different answer. I was wondering if you could tell me if I have the right answers or not. Thanks so much!
A certain air plane has 2 independent alternators to provide electrical power. The probability that one will fail is .02, what is the probability that.
(a) Probability both will fail = 0.0004
(b) Probability neither will fail (both will work fine) = 0.9604
(c) Probability one will fail = 0.0392
Problem 2:
A random sample of 10 miniature tootsie rolls was taken from a bag, each piece weighed on a very accurate scale. The results in grams were: 3.087 3.131 3.241 3.241 3.27 3.353 3.4 3.411 3.437 3.477
a)construct a 90% confidence interval for the true mean weight.
b)what sample size would be necessary to estimate the true weight with an error of .03 grams with 90% confidence.
c)discuss the factors which might cause variations in the weight of tootsie rolls during manufacturing.
Answers to a, b, and c:
A.
Sample mean 3.3048
Sample SD (s) 0.1320
Sample size (n) 10
Since sample size is smaller than 30, we will use a tdistribution.
Degree of freedom 9
Confidence level 90%
Critical tc 1.833
Margin of error 0.0765
Lower limit 3.2283
Upper limit 3.3813
B.
Margin of error 0.03
Confidence level 90%
Critical tc 1.833
SD 0.1320
Required sample size 65.04451373
Rounded up 6o 66.
C.
Factors include:machines that divide the raw material cannot divide perfectly equally. Although each was weighed on a very accurate scale there is still error of measurement. The temperature utilized during candy manufacture, sharpness of cutting tools utilized to form pieces.

Problem 2:
A random sample of 10 miniature tootsie rolls was taken from a bag, each piece weighed on a very accurate scale. The results in grams were: 3.087 3.131 3.241 3.241 3.27 3.353 3.4 3.411 3.437 3.477
a)construct a 90% confidence interval for the true mean weight.
b)what sample size would be necessary to estimate the true weight with an error of .03 grams with 90% confidence.
c)discuss the factors which might cause variations in the weight of tootsie rolls during manufacturing.
Answers to a, b, and c:
A.
Sample mean 3.3048
Sample SD (s) 0.1320
Sample size (n) 10
Since sample size is smaller than 30, we will use a tdistribution.
Degree of freedom 9
Confidence level 90%
Critical tc 1.833
Margin of error 0.0765
Lower limit 3.2283
Upper limit 3.3813
B.
Margin of error 0.03
Confidence level 90%
Critical tc 1.833
SD 0.1320
Required sample size 65.04451373
Rounded up 6o 66.
C.
Factors include:machines that divide the raw material cannot divide perfectly equally. Although each was weighed on a very accurate scale there is still error of measurement. The temperature utilized during candy manufacture, sharpness of cutting tools utilized to form pieces.