The mean of the data set is 40 and one standard deviation is 5. About what percent of the numbers fall between 35 and 50?53.2%68.2%77.4%81.8%

Answer:The correct option is D. 81.8%Step-by-step explanation:Mean of the data set is given to be 40⇒ μ = 40Standard deviation of the data set is given to be 5⇒ σ = 5Now we are supposed to find out what percent of the numbers fall between 35 and 50[tex]\implies z =\frac{x-\mu}{\sigma}[/tex]Now for P(35 < x < 50) :Substitute x = 35 ⇒ z = -1Substitute x = 50 ⇒ z = 2So, P(-1 < z < 2) = P(z < 2) - P(z < -1)⇒ P(-1 < z < 2) = 0.9772 - 0.1587⇒ P(-1 < z < 2) = 0.8185⇒ P(-1 < z < 2) = 81.8%Therefore, 81.8% percent of the numbers fall between 35 and 50Hence, The correct option is D. 81.8%