The yield strength of a steel rods manufactured by a certain company is under in
ID: 3220661 • Letter: T
Question
The yield strength of a steel rods manufactured by a certain company is under investigation. Five rods are selected at random and their yield strengths are measured. The sample mean is 460 MPa and the sample standard deviation is 16 MPa. Assume that the measurements are independent and that the yield strength follows a normal distribution.
(a) What is the probability that the sample mean is more than 20 MPa above the true mean yield strength?
(b) How would the result of part a) change if the standard deviation of 16 MPa were assumed to be known?
(The t-table should be used)
Explanation / Answer
a) here std error of mean =std deviation/(n)1/2 =7.1554
hence P(X>20+460) = 1-P(X<480)=1-P(T<(480-460)/7.1554)=1-P(T<2.795)=1-0.9755 =0.0245
if we know population std deviation then z distributionj will be used
b)P(X>480)=1-P(Z<2.795)=1-0.9974=0.0026
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