Question

before a chair manufacturer sells its beanbag chairs, they spot check a random sample of chairs on the production line. the table below shows the number of common problems found during one such spot check.

common problems	frequency
cuts in upholstery	14
understuffed	15
none	267
total	300

if the manufacturer makes 1500 beanbag chairs per day, how many of those chairs would they expect to be understuffed?
o they would expect 15 chairs to be understuffed.
o they would expect 75 chairs to be understuffed.
o they would expect 300 chairs to be understuffed.
o they would expect 750 chairs to be understuffed.

Explanation:

Step1: Calculate the proportion of under - stuffed chairs in the sample

The proportion $p$ of under - stuffed chairs in the sample of $n = 300$ chairs is calculated by dividing the number of under - stuffed chairs in the sample by the total number of chairs in the sample. The number of under - stuffed chairs in the sample is $15$, so $p=\frac{15}{300}=0.05$.

Step2: Estimate the number of under - stuffed chairs in the daily production

The manufacturer makes $N = 1500$ chairs per day. To find the expected number of under - stuffed chairs $E$, we multiply the proportion of under - stuffed chairs in the sample by the total number of chairs produced per day. So $E = p\times N=0.05\times1500 = 75$.

Answer:

They would expect 75 chairs to be understuffed.