Question

Problem 3-25 (Algorithmic) The College Board National Office recently reported that in 2011–2012, the 547,038 high school juniors who took the ACT achieved a mean score of 540 with a standard deviation of 122 on the mathematics portion of the test (http://media.collegeboard.com/digitalServices/pdf/research/2013/TotalGroup-2013.pdf). Assume these test scores are normally distributed.

What is the probability that a high school junior who takes the test will score no higher than 470 on the mathematics portion of the test? If required, round your answer to four decimal places.

P (x ≤ 470) =

What is the probability that a high school junior who takes the test will score between 470 and 550 on the mathematics portion of the test? If required, round your answer to four decimal places.

P (470 ≤ x ≤ 550) =

Answer 1

Solution :

Given that ,

mean = = 540

standard deviation = =122

P(x 470)

= P[(x - ) / (470 - 540) /122 ]

= P(z -0.5738)

= 0.2831

P(x 470) = 0.2831

P (470 x 550)

= P[(470 - 540 / 122) (x - ) / (550 - 540 / 122) ]

= P(-0.5738 z 0.0820)

= P(z 0.0820) - P(z -0.5738)

= 0.5327 - 0.2831

= 0.2496

P (470 x 550) = 0.2496