assume a member is selected at random from the population represented by the graph. find the probability…

assume a member is selected at random from the population represented by the graph. find the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed. standardized test composite scores 28 < x < 32 μ = 19.6 σ = 5.6 the probability that the member selected at random is from the shaded area of the graph is (round to four decimal places as needed.)

assume a member is selected at random from the population represented by the graph. find the probability that the member selected at random is from the shaded region of the graph. assume the variable x is normally distributed. standardized test composite scores 28 < x < 32 μ = 19.6 σ = 5.6 the probability that the member selected at random is from the shaded area of the graph is (round to four decimal places as needed.)

Answer

Explanation:

Step1: Calculate z - scores

Use the formula $z=\frac{x - \mu}{\sigma}$. For $x = 28$, $z_1=\frac{28 - 19.6}{5.6}=\frac{8.4}{5.6}=1.5$. For $x = 32$, $z_2=\frac{32 - 19.6}{5.6}=\frac{12.4}{5.6}\approx2.21$.

Step2: Find probabilities from z - table

We know that $P(28<X<32)=P(1.5 < Z < 2.21)$. From the standard - normal table, $P(Z < 2.21)=0.9864$ and $P(Z < 1.5)=0.9332$.

Step3: Calculate the probability of the interval

$P(1.5 < Z < 2.21)=P(Z < 2.21)-P(Z < 1.5)=0.9864 - 0.9332=0.0532$.

Answer:

$0.0532$