Power +, Inc produces AA batteries used in remote-controlled toy cars 1 he mean

Question

Power +, Inc produces AA batteries used in remote-controlled toy cars 1 he mean life or these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours As a part of its quality assurance program. Power + Inc tests samples of 9 batteries What can you say about the shape of the distribution of the sample mean? What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.) What proportion of the samples will nave a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) What proportion of the sample win nave a mean useful life greater than 34 5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.) What proportion, of the sample will have a mean useful life between 34 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Explanation / Answer

a.The sampling distribution of sample mean is also normal.

In probability theory, the central limit theorem states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined expected value and well-defined variance, will be approximately normally distributed, regardless of the underlying distribution.

b.The standard error of sample mean is:

s/root over n

=5.5/root over 9

=1.83

c.For X=38, z=(x-mu)/sigma

=(38-36)/1.83

=1.09

Thus, P(X>38)=P(z>1.09)=1-P(z<1.09)=1-0.8621=0.1379

d.For X=34.5, z=(34.5-36)/1.83

=-0.82

P(X>34.5)=P(z>-0.82)=1-P(z<-0.82)=1-0.2061=0.7939

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.