Question

A random sample of 48 was taken from a shipment of 10,080 light bulbs from Light Bulbs Express. Out of the 48 light bulbs, 5 were red. How many red bulbs would you expect in the entire shipment?

______________red bulbs (Round answer to the nearest whole number).




A random sample of 62 was taken from another shipment of 15,500 from Light Bulbs R Us. There were 6 red bulbs in the sample. How many red bulbs would you expect in the entire shipment?


_____________red bulbs (Round answer to the nearest whole number)




Which company has the highest ratio of red bulbs in their shipment?


Company ______ (Type either A or B)


Company A = Light Bulbs Express


Company B = Light Bulbs R Us

Answer 1

1. Expected(Red) in Shipment A = 1,050

2. Expected(Red) in Shipment B = 1,500

3. Company A has highest ratio of red bulbs

Explanation:

Given

Shipment A (Light Bulb Express):

Total Light Bulb = 10,080

Sample Size = 48

Red Bulbs = 5

To calculate the expected number of Red bulbs;

We start by calculating the probability of Red;

P(Red) = Number of Red / Sample Size

P(Red) = 5/48

Expected Number of Red Bulbs is calculated as follows;

Expected(Red) = P(Red) * Total Light Bulb

Expected(Red) = 5/48 * 10,080

Expected(Red) = 50400/48

Expected(Red) = 1,050

Hence, the expected number of red light bulbs in the entire shipment is 1,050

Given

Shipment B (Light Bulb R Us):

Total Light Bulb = 15,500

Sample Size = 62

Red Bulbs = 6

To calculate the expected number of Red bulbs;

We start by calculating the probability of Red;

P(Red) = Number of Red / Sample Size

P(Red) = 6/62

Expected Number of Red Bulbs is calculated as follows;

Expected(Red) = P(Red) * Total Light Bulb

Expected(Red) = 6/62 * 15,500

Expected(Red) = 93000/62

Expected(Red) = 1,500

Hence, the expected number of red light bulbs in the entire shipment is 1,050

The company with highest probability has the highest ratio;

For Company A (Light Bulb Express)

Probability = 5/48

Probability = 0.1042

For Company B (Light Bulb R Us)

Probability = 6/62

Probability = 0.0968

Since 0.1042 is greater than 0.0968, we can conclude that Company A has the highest ratio of red bulbs;