Question

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Answer 1

sample mean = 21.7 minutes

standard deviation = 4.8 minutes

sample size n = 45

standard error = standard deviation / sqrt (n)

= 4.8 / sqrt(45) = 0.71554

We know that X is normally distributed, with parameters:

μ=21.7, S.E=0.71554

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.1.

Mathematically, x is such that:

$\Pr(X \le x) = 0.1$

The corresponding z score so that the cumulative standard normal probability distribution is 0.1 is

This value of z_c = 1.2816 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.1 cumulative probability is

$x = \mu + z_c \times \sigma = 21.7 + (-1.2816) \times 0.71554$

= 21. 7 - 0.917036

= 20.782

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