Question

The scores of the students on a standardized test are normally distributed, with a mean of 500 and a standard deviation of 110. What is the probability that a randomly selected student has a score between 350 and 550

Answer 1

Answer:

The probability that a randomly selected student has a score between 350 and 550  = 0.5867

Step-by-step explanation:

Mean $(\nu )$ = 500

Standard deviation $(\sigma )$ = 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  =

$P(350< X< 550)$  = $P(\frac{ 350 - 500 }{110 }< \frac{ X - \nu }{\sigma }< \frac{ 550 - 500 }{110 } )$

                              = $P(- 1.36< Z< 0.45 )$       Putting   $(Z =\frac{ X - \nu }{\sigma })$

                              = $(Z< 0.45) - (Z< -1.36)$

                              = 0.6736 - .0869     ( Using Z table )

                              = 0.5867