Suppose that the lifetimes of light bulbs are approximately normally distributed

Question

Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions. (a) What proportion of light bulbs will last more than 60 hours? (b) What proportion of light bulbs will last 50 hours or less? (c) What proportion of light bulbs will last between 59 and 62 hours? (d) What is the probability that a randomly selected light bulb lasts less than 45 hours? (a) The proportion of light bulbs that last more than 60 hours is

Explanation / Answer

mean = 57

standard deviation = 3.5

a)

z value for 60 is (60-57)/3.5 = 3/3.5 = 0.8571 correspoding p value using z table is 0.8043

P(X<60) = 0.8043

P(X>60) = 1-0.8043 = 0.1957

proportion of light bulbs will last more than 60 hours = 0.1957

b)

z value for 50 is (50-57)/3.5 = -7/3.5 = -2 correspoding p value using z table is 0.0228

P(X<50) = 0.0228

proportion of light bulbs will last 50 hours or less = 0.0228

c)

z value for 59 is (59-57)/3.5 = 2/3.5 = 0.5714 correspoding p value using z table is 0.7161

P(X<59) = 0.7161

z value for 62 is (62-57)/3.5 = 5/3.5 = 1.4286 correspoding p value using z table is 0.9234

P(X<62) = 0.9234

P(59<X<62) = 0.9234-0.7161 = 0.2073

proportion of light bulbs between 59 and 62 hours = 0.2073

d)

z value for 45 is (45-57)/3.5 = -12/3.5 = -3.428 correspoding p value using z table is 0.0003

P(X<45) = 0.0003

probabty that randomly selcted bul lasts less than 45 hours is 0.0003

proportion of light bulbs will last 50 hours or less = 0.0228

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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