Question

the distribution of weight for 9 - ounce bags of a particular brand of potato chips can be modeled by a normal distribution with mean $mu = 9.12$ ounces and standard deviation $sigma=0.05$ ounce. sketch the normal density curve. label the mean and the points that are 1, 2, and 3 standard deviations from the mean. do not round your answers.

Explanation:

Step1: Calculate 1 - standard - deviation points

The formula to find the points that are \(k\) standard deviations from the mean \(\mu\) is \(x=\mu\pm k\sigma\). For \(k = 1\), \(x_1=\mu-\sigma=9.12 - 0.05=9.07\) and \(x_2=\mu+\sigma=9.12 + 0.05=9.17\)

Step2: Calculate 2 - standard - deviation points

For \(k = 2\), \(x_3=\mu-2\sigma=9.12-2\times0.05=9.12 - 0.10 = 9.02\) and \(x_4=\mu + 2\sigma=9.12+2\times0.05=9.12 + 0.10=9.22\)

Step3: Calculate 3 - standard - deviation points

For \(k = 3\), \(x_5=\mu-3\sigma=9.12-3\times0.05=9.12 - 0.15=8.97\) and \(x_6=\mu+3\sigma=9.12+3\times0.05=9.12 + 0.15=9.27\)
The mean is \(\mu = 9.12\).

Answer:

Label the mean as \(9.12\). Label the points: \(8.97\) (3 standard - deviations below the mean), \(9.02\) (2 standard - deviations below the mean), \(9.07\) (1 standard - deviation below the mean), \(9.17\) (1 standard - deviation above the mean), \(9.22\) (2 standard - deviations above the mean), \(9.27\) (3 standard - deviations above the mean)