Can someone help me which way can I approach this problem. A hint of a formula or anything would be helpful...
Life of Light Bulbs A certain type of light bulb has an average
life 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. An amusement park buys and installs 10,000 such
bulbs. Find the total number that can be expected to last for
each period of time.
The question is:
Find the shortest and longest lengths of life for the middle 80% of the bulbs.
I suggest you use the helpful tool at
http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
Enter 500 for mean and 100 for std deviation. Then enter pairs of numbers for the upper and lower limits that are symmetrical bout 500. Hit
"Enter" to see that part of the distribution curve corresponding to those limits. I get 372 to 628 hours, corresponding to 80% of the bulbs, with 10% burning out earlier than 372 hours and 10% later than 628 hours.
To approach this problem, we need to find the shortest and longest lengths of life for the middle 80% of the bulbs.
To do this, we can use the concept of the normal distribution. The given information tells us that the average life of the light bulb is 500 hours and the standard deviation is 100 hours. Since the length of life of the bulb follows a normal curve, we can calculate the bounds within which the middle 80% of the bulbs will fall.
To find these bounds, we can use a normal distribution calculator. The suggested website, http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html, is one such tool that can assist us.
On the website, enter the mean of 500 and the standard deviation of 100. Then, enter pairs of numbers for the upper and lower limits that are symmetrical about 500. This means that the difference between the lower limit and 500 should be the same as the difference between 500 and the upper limit.
Click on "Enter" to visualize the part of the distribution curve corresponding to those limits. The website should show you the percentage of bulbs within those limits.
According to the solution provided, the shortest and longest lengths of life for the middle 80% of the bulbs are 372 hours and 628 hours, respectively. This means that 10% of the bulbs will burn out earlier than 372 hours, and another 10% will last longer than 628 hours.