MATH SOLVE

5 months ago

Q:
# weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of 50$. find the probability that a worker selected at random makes between $350 and $400.

Accepted Solution

A:

Answer:0.34134Step-by-step explanation:In other to solve for this question, we would be using the z score formulaz = (x - μ) / σ x = raw scoreμ = meanσ = Standard deviationWe are told in the question to find the probability that a worker selected at random makes between $350 and $400 let x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50. z1 = (x1 - μ) / σ = (350-400) / 50 = -1z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0From tables, P(z <= -1) = 0.15866 P(z <= 0) = 0.5Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134