Question

question 5 1 pts if continuous random variable x is normally distributed with μ = 5625 and σ = 875.5, what is p(5000 ≤ x ≤ 6000)? 90.53% 42.75% 9.47% 47.72%

Explanation:

Step1: Calculate z - scores

For \(x = 5000\), \(z_1=\frac{5000 - 5625}{875.5}=\frac{- 625}{875.5}\approx - 0.714\)
For \(x = 6000\), \(z_2=\frac{6000 - 5625}{875.5}=\frac{375}{875.5}\approx0.428\)

Step2: Use z - table

\(P(-0.714<Z<0.428)=\Phi(0.428)-\Phi(- 0.714)\)
From the standard normal table, \(\Phi(0.428)\approx0.665\), \(\Phi(-0.714) = 1-\Phi(0.714)\approx1 - 0.762 = 0.238\)
\(P(-0.714<Z<0.428)=0.665 - 0.238=0.427\) or \(42.7\%\approx42.75\%\)

Answer:

C. 42.75%