Question

Manufacturing companies strive to maintain production​ consistency, but it is often difficult for outsiders to tell whether they have succeeded. Consider a company that makes a certain brand of candy claims that 8​% of the candies it produces are yellow and that bags are packed randomly. Their production controls can be checked by sampling bags of candies. Suppose bags containing about 300 candies are opened and the proportion of yellow candies is recorded.

Question: It's appropriate to use normal model because np=______ and nq=_______

Question: About 68% of the bags will have between _____% and ______% orange candles.

Question: About 95% of the bags will have between _____% and _______% orange candles.

Question: About 99.7% of the bags will have between ______% and ______% orange candles.

Answer 1

P(yellow candy), p = 0.08

q = 1 - p = 0.92

Sample size, n = 300

np = 300x0.08 = 24

nq = 300x0.92 = 276

np and nq > 10. So, it is appropriate to use normal model.

Mean, of sample proportion = 8

Standard deviation of sample proportion =

=

= 0.0157

According to the empirical rule, 68%, 95% and 99.7% of the data values lie within 1, 2 and 3 standard deviations of mean.

About 68% of the bags will have between 8-0.0157 = 7.9843% and 8+0.0157 = 8.0157% yellow candies.

Question: About 95% of the bags will have between 8-2x0.0157 = 7.9687% and 8+2x0.0157 = 8.0313% yellow candies.

Question: About 99.7% of the bags will have between 8-3x0.0157 = 7.9529% and 8+3x0.0157 = 8.0471% yellow candies.