Question

During the 52 week period ranging from 01/01/2002 to 12/30/2002, a bottle manufacturing company tracked the number of cases (of bottles) it lost in transit on a weekly basis. The average number of cases lost per week was 30.8 with a standard deviation of 2.6. The number of weeks in which it lost more than 36 cases, absent any additional information or assumption, is

Answer 1

The number of weeks in which the bottle manufacturing company lost more than 36 cases is expected to be very small, with a probability of only 0.57%.

Step-by-step explanation:

To determine the number of weeks in which the bottle manufacturing company lost more than 36 cases, we need to calculate the z-score for 36 cases lost and find the probability of getting a value greater than that.

The z-score can be calculated using the formula: z = (x - μ) / σ, where x is the value (36), μ is the mean (30.8), and σ is the standard deviation (2.6).

After calculating the z-score, we can use a standard normal distribution table or calculator to find the probability. The probability is the area under the curve to the right of the z-score.

The calculated z-score is 2.5385. Looking up this value in a standard normal distribution table, we can determine that the probability of getting a value greater than 36 is approximately 0.0057, or 0.57%.

Therefore, the number of weeks in which the company lost more than 36 cases is expected to be very small, with a probability of only 0.57%.

Answer 2

approximately 2 weeks

Step-by-step explanation:

Assuming normal distribution, we have

mean m = 30.8

standard deviation s = 2.6

The standard random variable is given by Z = (x - 30.8)/2.6

where x denotes the number of cases lost

we are to evaluate probability of losing more than 36 i.e P(x > 36)

This will be P(Z > (36 - 30.8)/2.6) = P(Z > 2)

using the z-score table, we have this probability to be 0.0228

so the number of weeks is given by 52*0.228 = 1.19

which is approximately 2