Suppose commute times in a large city are normally distributed and that 65.20% of commuters in this city take more than 20 minutes to commute one-way. if the standard deviation of such commutes is 6.3 minutes, what is the mean commute?

The mean time for commute is 22.46 minutes.

Step-by-step explanation:

We are given the following information in the question:

Standard Deviation, σ = 6.3 minutes

We are given that the distribution of commute times in a large city is a bell shaped distribution that is a normal distribution.

Formula:

P(more than 20 minutes to commute one-way)  = 65.20% = 0.6520

P(X > 20) = 0.6520

Calculation the value from standard normal z table, we have,  

Solving, we get,

The mean time for commute is 22.46 minutes.

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