Answer:
The value is [tex]\sigma = 31.35[/tex]
Step-by-step explanation:
From the question we are told that
The average score is [tex]\mu = 60[/tex]
Generally the probability that [tex]\frac{1}{4} = 0.25[/tex] of the class score is between 50 and 70 points is mathematically represented as
[tex]P(50 < X < 70)= P(\frac{50 - 60 }{\sigma } < \frac{X - \mu }{\sigma} < \frac{70 - 60}{\sigma } ) = 0.25[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
So
[tex]P(50 < X < 70)= P(\frac{-10 }{\sigma } < Z < \frac{10}{\sigma } ) = 0.25[/tex]
=> [tex]P(50 < X < 70)= P(Z < \frac{10 }{\sigma }) -(Z < \frac{-10}{\sigma } )= 0.25[/tex]
=> [tex]P(50 < X < 70)= 2P(Z < \frac{10 }{\sigma }) = 0.25[/tex]
From the normal distribution table the critical value of 0.25 for a two tailed test is z= 0.318
So
[tex]\frac{10}{\sigma } = 0.319[/tex]
=> [tex]\sigma = 31.35[/tex]
