Answer:
The probability that a randomly selected student has a score between 350 and 550 = 0.5867
Step-by-step explanation:
Mean [tex](\nu )[/tex] = 500
Standard deviation [tex](\sigma )[/tex] = 110
Let X be the score of student in a standardized test
The probability that a randomly selected student has a score between 350 and 550 =
[tex]P(350< X< 550)[/tex] = [tex]P(\frac{ 350 - 500 }{110 }< \frac{ X - \nu }{\sigma }< \frac{ 550 - 500 }{110 } )[/tex]
= [tex]P(- 1.36< Z< 0.45 )[/tex] Putting [tex](Z =\frac{ X - \nu }{\sigma })[/tex]
= [tex](Z< 0.45) - (Z< -1.36)[/tex]
= 0.6736 - .0869 ( Using Z table )
= 0.5867
