Question

The Radclie Chemical Company produces explosives for Because of the nature of its products, the company devot safety, which is also scrutinized by the federal governme show that the annual number of property damage and pe accidents is normally distributed, with a mean of 8.3 acc deviation of 1.8 accidents. What is the probability that the company will have next year? more than 10? (b)The government will fine the company $200,000 if th accidents exceeds 12 in a 1-year period. What average an company expect?​

Answer 1

(a) The probability of having more than 10 accidents is approximately P(Z > 0.944).

(b) The expected number of accidents for which the government will impose a fine of $200,000 is approximately 12.0008.

(a) Probability of More Than 10 Accidents:

Calculate the z-score:

z = (10 - 8.3) / 1.8

`\[ z \approx 1.7 / 1.8 \approx 0.944 \]`

Now, using a standard normal distribution table or calculator, find the probability associated with a z-score of 0.944, let's say P(Z > 0.944).

(b) Expected Fine for Exceeding 12 Accidents:

z = (12 - 8.3) / 1.8

`\[ z \approx 3.7 / 1.8 \approx 2.056 \]`

Again, using the standard normal distribution table or calculator, find the probability associated with a z-score of 2.056, let's say P(Z > 2.056).

Now, to calculate the expected number of accidents (N) for 12 accidents:

`\[ N_(12) = 8.3 + 2.056 * 1.8 \]`

Now, let's substitute the values and calculate:

`\[ N_(12) = 8.3 + 2.056 * 1.8 \]`

`\[ N_(12) = 8.3 + 3.7008 \]`

`\[ N_(12) \approx 12.0008 \]`

Please note that for precise values, you may use a standard normal distribution table or a statistical calculator.