A certain type of Christmas light bulb has an average life span of 500 hours, wi

Question

A certain type of Christmas light bulb has an average life span of 500 hours, with a standard deviation of 100 hours. The length of life of the bulb can be closely approximated by a normal curve. Santa's Light Delight uses 1,000,000 of these bulbs in their displays. Find the total number of bulbs that can be expected to last for each period of time a) At most 550 hours. b Between 325 and 750 hours. c) At least 650 hours In the United States of America, the average newborn baby weighs 7.5 pounds. The standard deviation on these weights is 1.2 pounds. In what weight range, rounded to the nearest tenth of a pound, do 90% of the babies born in the United States of America fall?

Explanation / Answer

Q.15

The average life span = 500 hours and

standard deviation = 100 Hours

(a) First we have to calculate the expected number of bulb to last at most 550 Hours

so first we will calculate the probability of a bullb to last at most 550 years.

Pr( X <= 550 ; 500; 100) = ?

Z - value => Z = (550- 500)/ 100 = 0.5

Pr( X <= 550 ; 500; 100) = (0.5)

where is the cumuative normal probability function

soPr( X <= 550 ; 500; 100) = (0.5) = 0.6915

so Expected number of bulbs out of 1 million will last = 10,00,000 * 0.6915 = 69,1500

(b) Betwenn 325 and 750 Hours

so Pr (325 <= X < = 750; 500 ; 100) = Pr( X <= 750; 500 ; 100) - Pr ( X <= 325 ; 500 ; 100)

calculation Z - values for X = 750 and 325

Z = (750 - 500)/ 100 = 2.5 and z = ( 325 - 500)/100 = -1.75

Pr (325 <= X < = 750; 500 ; 100) = (2.5) - ( -1.75) = 0.9938 - 0.0401 = 0.9537

so Expected number of bulbs will last in between these times= 10,00,000 * 0.9537 = 953, 700

(c) At least 650 hours

Pr( X <= 650 ; 500; 100) = ?

Z - value => Z = (650- 500)/ 100 = 2.5

Pr( X <= 650 ; 500; 100) = (1.5)

where is the cumuative normal probability function

soPr( X <= 650 ; 500; 100) = (1.5) = 0.9332

so Expected number of bulbs out of 1 million will last = 10,00,000 * 0.9332 =93,3200

Q.16

We have to calculate 90% confidence interval for baby weights

so 90% CI = +- Z0.90 = 7.5 +- 1.645 * 1.2 = (5.526, 9.474)

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