Question

determine p(5≤x≤10)if the mean is 7 and the standard deviation is 1.1.
0.962
0.883
0.971
0.798

Explanation:

Step1: Calculate z - scores

For \(x = 5\), \(z_1=\frac{5 - 7}{1.1}=\frac{- 2}{1.1}\approx - 1.82\)
For \(x = 10\), \(z_2=\frac{10 - 7}{1.1}=\frac{3}{1.1}\approx2.73\)

Step2: Use standard normal distribution table

\(P(5\leq X\leq10)=P(-1.82\leq Z\leq2.73)\)
\(P(-1.82\leq Z\leq2.73)=P(Z\leq2.73)-P(Z\leq - 1.82)\)
From the standard - normal table, \(P(Z\leq2.73) = 0.9968\), \(P(Z\leq - 1.82)=0.0344\)

Step3: Calculate the probability

\(P(-1.82\leq Z\leq2.73)=0.9968 - 0.0344=0.9624\approx0.962\)

Answer:

\(0.962\)