Let X be the lifetime of an electronic device. It is known that the average life

Question

Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 798 days and the standard deviation is 116 days. Let x bar be the sample mean of the lifetimes of 229 devices. The distribution of X is unknown, however, the distribution of x bar should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation. (a) P (x bar lessthanorequalto 791) = (b) P (x bar greaterthanorequalto 805) = (c) P(784 lessthanorequalto x bar lessthanorequalto 813) = suppose that measurements of your systolic blood pressure are normally distributed with some unknown mean mu and

Explanation / Answer

We use the Z table to solve the problem:

a. P(Xbar<=791) = P(X<=(791-798)/(116/sqrt(229)) ) = P(Z<=-.91) = .1814

b. P(Xbar>=805) = P(X> (805-798)/(116/sqrt(229))) = P(Z>=.91) = 1-.8186 - .1814

c. P(784<=Xbar<=813) = P(-1.83<Xbar<1.96) = .95-.0335 = .9165

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

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