{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

homework_5_ans

# homework_5_ans - Course MTH 1210 Homework#5(answers(The...

This preview shows pages 1–2. Sign up to view the full content.

Course MTH 1210 Homework #5 ( answers ) ( The Normal Distribution ) Mar 24’09 Use the MS Excel program Three_distributions.xls, sheet 3 1. A certain type of light bulb has an average life of 500 hr , with a standard deviation of 100 hr . 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 of the following periods of time: (a) less than 500 hr, (b) between 290 and 540 hr, (c) more than 300 hr. Solution. In this problem we are given that the mean (average) µ = 500 hr and the standard deviation σ = 100 hr. Run the program Three_distributions.xls, sheet 3 and enter the values of 500 and 100 in the cells G58 and G59 respectively (type in each value and press [ENTER] key). We’ll work with the rectangular block of cells E53 – K62 . (a) To answer this question, we should evaluate the product 10,000*f(X ≤ 500) where f(X ≤ 500) is the cumulative probability that the length of life of a bulb is less than or equal to 500 hr. Enter the value of 500 in the cell G58 for x . We find that f(X ≤ x) = 0.5 (see the cell I59 ). Thus, 10,000*f(X ≤ 500) = 10,000*0.5 = 5000 . x = 500 f(x) = 0.003989 µ = 500 σ = 100 f(X ≤ x) = 0.5 (b) The number in question is 10,000*f(290 ≤ X ≤ 540) = 10,000*[ f(X ≤ 540) – f(X ≤ 290) ]. To evaluate the cumulative probability f(X ≤ 540) that the length of life of a bulb is less than or equal to 540 hr, we enter the value of 540 in the cell G58 for x and find in the cell I59 that f(X ≤ x) = 0.655422 . x =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

homework_5_ans - Course MTH 1210 Homework#5(answers(The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online