Answer to Question #309251 in Statistics and Probability for sharmaione

Question

given the mean μ 124 and standard deviation is σ = 3. find the z-value that corresponds to a score X=118. then find and graph the proportion of the are greater than the computer z-value

Answer 1

given the mean $μ= 124$

standard deviation is $σ = 3$

(a)

$Z=\dfrac{X-\mu}{\sigma}=\dfrac{118-124}{3}$

$Z=-2.0$

(b) P value for $Z(-2.0)=0.02275$

$=2.275\%$

The proportion greater than the Z value (Z=-2.0)$=(100-2.275)\% = 97.725\%$

The proportion is shaded as shown below