Please answer in details showing the work. III. Lightbulbs produced by a company
ID: 340350 • Letter: P
Question
Please answer in details showing the work.
III. Lightbulbs produced by a company have a life expectancy that is normally distributed with u = 180 days and o = 8 days. a. What is the probability a bulb will last beyond 192 days? b. What is the probability a bulb will fail in 175 days or less? IV. A producer can produce a product at a variable cost per unit of $7. The producer can sell the product for $11 each. If the fixed cost is $70,000 a. How many units must the producer sell to break-even? b. What is revenue at 25,000 units? What is total cost at 25,000 units? c. How many units must the producer sell in order to earn a profit of $60,000?Explanation / Answer
Answer to question III :
Mean life expectancy = m = 180 days
Standard deviation of life expectancy = Sd = 8 days
Let Z value for the probability that a bulb will last maximum upto 192 days = Z1
Therefore,
M + Z1 x Sd = 192
Or, 180 + 8.Z1 = 192
Or, 8.Z1 = 12
Or, Z1 = 12/8 = 1.5
Corresponding probability for Z = 1.5 as derived from standard normal distribution table is 0.93319
Thus, probability that a bulb will last maximum 192 days = 0.93319
Therefore , probability that a bulb will last beyond 192 days
= 1 – Probability that a bulb will last maximum 192 days
= 1 – 0.93319
= 0.06681
Let z value corresponding to probability that bulb will last maximum 175 days or less = Z2
Therefore ,
M + Z2 x sd = 175
Or, 180 + 8.Z2 = 175
Or, 8.Z2 = - 5
Or, Z2 = - 0.625 ( - 0.63 rounded to 2 decimal places )
Corresponding probability for Z = - 0.63 as derived from standard normal distribution table 0.26435
Therefore , probability that a bulb will fail in 175 days or less = 0.26435
Answer to question IV :
Breakeven quantity
= Fixed cost per unit/ ( selling price per unit – variable cost per unit)
= 70,000/ ( 11 – 7)
= 70,000/4
= 17500
Revenue at 25000 units = Price/ unit x 25000 units = $11 x 25000 = $275000
Total cost at 25000 units = Cost / unit x 25000 units = $7 x 25000 = $175000
Let the quantity to be sold to earn a profit of $60,000 = N
Profit
= Total revenue – Total cost
= Price/ unit x Quantity sold – ( variable cost / unit x Quantity sold + Fixed cost )
= Quantity sold / unit x ( Price/ unit – Variable cost / unit ) – Fixed cost
Or.
60,000 = N x ( 11 – 7 ) – 70000
Or, 4.N = 130,000
Or, N = 32500
THE PRODUCER MUST SELL 32500 UNITS TOEARN A PROFIT OF $60,000