Answer to Question #262883 in Statistics and Probability for nero

Question

A survey conducted in Mega Manila with a sample of 500 gasoline stations found that the price charged per liter of gasoline is normally distributed with a mean of P55 and a standard deviation of P3. Using the empirical rule, determine the number of stations that charge between P50 and P54.

Answer 1

$n=500 \\ \mu=55 \\ \sigma= 3 \\ P(50<X<54) = P(X<54) -P(X<50) \\ =P(Z< \frac{54-55}{3}) -P(Z< \frac{50-55}{3}) \\ = P(Z< -0.333) -P(Z< -1.666) \\ = 0.3695 -0.0478 \\ = 0.3217 \\ N = 500 \times 0.3217 = 160.85 ≈ 161$

The number of stations that charge between P50 and P54 is 161.