10 soldiers of 500 attempt to climb a 100Ft cliff, they fail in : 57 ft, 73, 81, 78,63,85,41,68,75,88. What is probability of soldiers successfully climbing the cliff?

Calculate mean and standard deviation.

Z = (score - mean)/SD = (100-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the smaller proportion related to your Z score.

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To find the probability of soldiers successfully climbing the cliff, we need to determine the number of soldiers who successfully climbed and divide it by the total number of soldiers who attempted.

Given that 10 soldiers attempted to climb the cliff and the heights at which they failed are 57 ft, 73 ft, 81 ft, 78 ft, 63 ft, 85 ft, 41 ft, 68 ft, 75 ft, and 88 ft.

Step 1: Calculate the number of soldiers who successfully climbed the cliff.
To do this, we need to find the number of soldiers whose failed height is less than or equal to 100 ft (the height of the cliff).

The soldiers who failed at the following heights did not successfully climb the cliff:
57 ft, 73 ft, 81 ft, 78 ft, 63 ft, 85 ft, 41 ft, 68 ft, 75 ft, and 88 ft.

Therefore, the number of soldiers who successfully climbed the cliff is: 10 - 10 = 0.

Step 2: Calculate the probability of soldiers successfully climbing the cliff.
The probability is the number of successful outcomes divided by the total number of possible outcomes.

In this case, the number of successful outcomes is 0 (as no soldier successfully climbed the cliff) and the total number of possible outcomes is 10.

Therefore, the probability of soldiers successfully climbing the cliff is: 0/10 = 0.

Hence, the probability of soldiers successfully climbing the cliff is 0.