On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 403 pounds and a standard deviation of 67 pounds. The cow transport truck holds 4 cows and can hold a maximum weight of ______ pounds. Fill in the blank with the appropriate number.

Question

29-04-2024
Physics

High School

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On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 403 pounds and a standard deviation of 67 pounds. The cow transport truck holds 4 cows and can hold a maximum weight of ______ pounds. Fill in the blank with the appropriate number.

Answer :

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damonsalvator7878 damonsalvator7878 · Answer 1 · 2024-02-28T09:37:28-05:00

The cow transport truck can hold a maximum weight of approximately 1608 pounds.

To determine the maximum weight the cow transport truck can hold, we need to consider the weights of the four cows. Since the weights of cows on planet Cowabunga follow a normal distribution with a mean [tex]($ \mu $)[/tex] of 403 pounds and a standard deviation [tex]($ \sigma $)[/tex] of 67 pounds, we can use these parameters to calculate the total weight of four cows.

1. Calculation of Total Weight:

The total weight of four cows can be calculated by multiplying the mean weight by the number of cows. Since the mean weight of one cow is 403 pounds, the total weight of four cows is ( 4 × 403 = 1612 ) pounds.

2. Adjustment for Variability:

However, since the weights of cows follow a normal distribution with a standard deviation of 67 pounds, there is variability in the weights of individual cows. To account for this variability, we can use a rule of thumb that states that approximately 95% of the data lies within two standard deviations of the mean. Therefore, to be conservative, we subtract two standard deviations from the total weight of four cows.

3. Final Calculation:

Subtracting two standard deviations from the total weight, we get ( 1612 - 2 × 67 = 1612 - 134 = 1478 ) pounds. Thus, the cow transport truck can hold a maximum weight of approximately 1478 pounds to ensure that it can accommodate the weights of four cows with high certainty.