The commuters in the city follows a normal distribution.
The mean commute in the large city is 22.984
The given parameters are:
[tex]\mathbf{x = 21}[/tex] -- number of minutes
[tex]\mathbf{\sigma =6.2}[/tex] -- standard deviation
[tex]\mathbf{P(x > 21) =62.50\%}[/tex]
Using the complement rule
[tex]\mathbf{P(x \le 21) =1 - 62.50\%}[/tex]
[tex]\mathbf{P(x \le 21) =0.375}[/tex]
From z-table of probabilities, the z-score, when p value = 0.375 is:
[tex]\mathbf{z = -0.32}[/tex]
The z-score of a distribution is:
[tex]\mathbf{z = \frac{x - \mu}{\sigma}}[/tex]
Substitute known values
[tex]\mathbf{-0.32 = \frac{21 - \mu}{6.2}}[/tex]
Multiply both sides by 6.2
[tex]\mathbf{-1.984 = 21 - \mu}[/tex]
Collect like terms
[tex]\mathbf{\mu= 21 +1.984 }[/tex]
[tex]\mathbf{\mu= 22.984 }[/tex]
Hence, the mean commute is 22.984
Read more about normal probabilities at:
https://brainly.com/question/6476990
