Answer:
a. 0.07 or 7%
b. 0.1841 or 18%
c. 0.35 or 35%
d. 0%
Step-by-step explanation:
Given
Mean=μ=56 hours
and
Standard Deviation=σ=3.3 hours
In order to find the proportions of light bulbs we will have to find the z-scores.
The formula for z-score is:
z-score=(x-μ)/σ
So,
a) proportion of light bulbs that will last more than 61 hours
z-score=(61-56)/3.3
=5/3.3
=1.5151
The area to the left of z-score 1.5151 is 0.9344. As we have to caclculate the proportion of light bulbs greater than 61 hours.
Area to the right of z-score=1-0.9344
=0.0656
Rounding off to the nearest 10 will give us 0.07
7% of the bulbs will last more than 61 hours.
b) What proportion of light bulbs will last 53 hours or less?
z-score=(53-56)/3.3
=(-3)/3.3
=-0.9090
Area to the left of z-score is 0.18406. Rounding off will give us:
=0.1841
18% of the bulbs will last 53 hours or less.
c) What proportion of light bulbs will last between 57 and 62 hours?
z-score for 57=(57-56)/3.3
=1/3.3
=0.3030
The area to the left of z-score 0.3030 is 0.61791
z-score for 57=(62-56)/3.3
=6/3.3
=1.8181
The area to the left of z-score 1.8181 is 0.96485
Area between z-scores of 57 and 62=0.96485-0.61791
=0.34694
Rounding off gives 0.35
35% of the bulbs will last between 57 to 62 hours.
d) What is the probability that a randomly selected light bulb lasts less than 46 hours?
z-score for 46=(46-56)/3.3
=(-10)/3.3
=-3.0303
Area to the left of z-score is 0.00122. Rounding off gives 0.00. So almost zero percent of the bulbs will last less than 46 hours ..
