Question

Tony, a highway safety inspector, is concerned about the potential for accidents caused by boulders that fas down a sandstone cliff beside aimain highway. As part of an aceident simulator, Tony models the boulders' weights using a normal distribution with a mean of 567 kg and a standard deviatien of IS0 kg. Use this toble or the ALEKS caiculotor to find the percentege of boulders that weigh between 273 kg and 645 kg according to the model. far your intermediate. (computations, use four or more decimal places. Give your finat aniswer to two decimal places

Answer 1

To find the percentage of boulders that weigh between 273 kg and 645 kg according to the model, we can use the properties of the normal distribution. The result is approximately 0.9398 or 93.98%.

Step-by-step explanation:

To find the percentage of boulders that weigh between 273 kg and 645 kg according to the model, we can use the properties of the normal distribution.

We know that the mean weight of the boulders is 567 kg and the standard deviation is 150 kg.

To solve this, we can convert the weights to z-scores using the formula:

z = (x - mean) / standard deviation

Then, we can use a normal distribution table or calculator to find the percent of boulders within the given range. In this case, we want to find the area under the curve between z-scores -2.26 (for 273 kg) and 3.32 (for 645 kg). The result is approximately 0.9398 or 93.98%.