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A taxi company reveals that the daily earnings of taxi drivers in the company follows a normal distribution with a mean of $1062.5 and standard deviation of $350. (a) Find the probability that a taxi driver earns less than $1500 in a day

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Final answer:

To find the probability of a taxi driver earning less than $1500, we calculate the Z-score with the provided mean and standard deviation, and then look up this Z-score in a standard normal distribution table or use a calculator to find the associated probability.

Step-by-step explanation:

To calculate the probability that a taxi driver earns less than $1500 in a day, we need to normalize this problem using a Z-score formula since the earnings follow a normal distribution with a mean of $1062.5 and a standard deviation of $350. The Z-score is calculated as follows:

Z = (X - µ) / σ

Where X is the value we're looking for the probability of ($1500), µ is the mean ($1062.5), and σ is the standard deviation ($350).

Z = ($1500 - $1062.5) / $350

Z = $437.5 / $350

Z = 1.25

Using a standard normal distribution table or calculator, we would look up the probability associated with a Z-score of 1.25, which gives us a probability value. This value represents the chance that a taxi driver earns less than $1500 in a day.

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