Question

Bus trip times between 2 stops on a certain route are normally distributed with a mean of 5.7 minutes and a standard deviation of 1.5 minutes. What is the trip time that constitutes the 35th percentile? Express your answer correct to 1 decimal place and add the units (minutes) /content/enforced/490502-MATH210002_2020W/z-table-1.pdf

Answer 1

Answer is:

${\color{DarkRed} 6.3 \text{ minutes}}$

Calculations

We know that X is normally distributed, with parameters:

$\mu = 5.7, \text{ } \sigma = 1.5$

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.35. Mathematically, x is such that:

$\Pr(X \le x) = 0.35$

The corresponding z score so that the cumulative standard normal probability distribution is 0.35 is

This value of zc​=0.3853 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.35 cumulative probability is

$x = \mu + z_c \times \sigma = 5.7 + 0.3853 \times 1.5 = 6.278 \sim 6.3 \text{ minutes}$

Graphically:

$normaldistributiongrapher.php?mean=5.7&s$

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