The average drive to work is 9.6 miles. Assume standard deviation is 1.8. If random sample of 36 employed who derive to work are selected, find the probability that mean of sample miles driven to work is between 9 and 10 miles.

The average drive to work is 9.6 miles and the standard deviation is 1.8, which describes the spread of data around the mean. To calculate probability that mean of sample miles driven to work is between 9 and 10 miles, we first need to calculate z-score for these two means which are 9 and 10 respectively.

The average drive to work is 9.6 miles. Assume standard deviation is 1.8. If random sample of 36 employed who derive to work are selected, find the probability that mean of sample miles driven to work is between 9 and 10 miles.

The z-score can be calculated using the formula ,
Z = (x – μ) / σ , where x=sample mean , μ = population mean and σ = population standard deviation .
In our case, x=9 & 10 , μ = 9.6 &σ =1.8 . The Z scores for each sample becomes:

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