A population of values has a normal distribution with \mu=13.2 and \sigma=5.

Question

A population of values has a normal distribution with $μ = 13.2$ and $σ = 5$ . You intend to draw a random sample of size $n = 60$ .
Find the probability that a single randomly selected value is between 11.5 and 14.
$P (11.5 < X < 14) =$ ?
Write your answers as numbers accurate to 4 decimal places.

Answer 1

The probability that a single randomly selected value is between 11.5 and 14 is 0.1966, which is obtained below:
$P (x_{1} < X < x_{2}) = P (\frac{x_{1} - μ}{σ} < z < \frac{x_{2} - μ}{σ})$
$P (11.5 < X < 14) = P (\frac{11.5 - 13.2}{5} < z < \frac{14 - 13.2}{5})$
$= P (- 0.340 < z < 0.160)$
$= P (z < 0.160) - P (z < - 0.340) [U s e s t a n d a r d n o r m a l t a b l e]$
$= 0.56356 - 0.36693 = 0.1966 .$

A population of values has a normal distribution with \mu=13.2 and \sigma=5.

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