Answer to Question #130556 in Statistics and Probability for Samuel kassapa

Question

The weights of bags of chips produced by Baaba’s Snacks has a bell-shaped distribution with a mean of 20 ounces and a standard deviation of 0.07 ounces.
Use this information to answer questions 7, 8 and 9.

Approximately 68% of chips bags weigh between:

Approximately what percentage of chips bags weigh between 19.86 and 20.07 ounces?


If 200 chips bags are selected at random, about how many do you expect to weigh more than 20.14 ounces?

Answer 1

It is given to us that the weights of bags of chips produced by Baaba’s Snacks has a bell-shaped distribution which can be represented as under-

$\mu = 20$

$\sigma = 0.07$

ANSWER 1)

From the above figure (or property of a standard normal distribution) we can say that approximately 68% of the chip bags weigh between 1 standard deviation on the left of the mean and 1 standard deviation on the right of the mean.

whose interval is given by,

20 - 0.07, 20 + 0.07

Hence, approximately 68% of chips bags weigh between :19.93 and 20.07 ounces.

ANSWER 2)

It is asked to find the % population between 19.86 and 20.07 ounces which can be interpreted as 2 standard deviations on the left of the mean and 1 standard deviation on the right of the mean.

From the figure its value = (95.5/2) + (68.3/2) = 81.9%

Approximately 81.9% of chips bags weigh between 19.86 and 20.07 ounces.

ANSWER 3)

The % population of chip bags weighing more than 20.14 ounces can be interpreted as the % population more than the 2 standard deviations on the right of the mean = 50 - (95.5/2) = 2.25%

Since the sample size is 200, 2.25% of the sample size = 4.5 samples which means,

Approximately 4 or 5 samples of 200 samples weigh more than 20.14 ounces.