Question

In 2017, the SAT scores in the US has a mean of 1060 and a standard deviation of 195.

If a student is randomly selected, what is the probability that his/her score is less than 900? round your answer to 3 decimal places.

If a college only consider applicants with SAT scores from the top 10% what is the cutoff score ? round your answer to the nearest whole number.

If a random sample of 100 students is selected, what is the probability that the mean score is between 1100 and 1400 round your answer to 3 decimal places

Answer 1

Solution :

Given that ,

P(x < 1060)

= P[(x - ) / < (900 - 1060) / 195]

= P(z < - 0.82)

Using z table,

= 0.206

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28) = 0.90  

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 195 +1060

x = 1309

n = 100

= 1060

= / n = 195 / 100 = 19.5

P(1100< < 1400)  

= P[(1100 - 1060) / 19.5 < ( - ) / < (1400 - 1060) / 19.5)]

= P(2.05 < Z < 17.44)

= P(Z < 17.44) - P(Z < 2.05)

Using z table,  

= 1 - 0.980  

= 0.020