The Graduate Record Examinations are widely used to help predict the performance of applicants to graduate schools. The range of possible scores on the capital of GRE is 200 to 900. The psychology department at a university finds that the scores of its applicants on the quantitative GRE are approximately normal with mean = 544 and population standard deviation = 103. Use the z-table to find the probability of applicants who score is between 500 and 700.(Please write your answer as a decimal. The testing system is not able to recognize a % sign. So if you have 1.23% then this should be written as .0123 which is the decimal equivalent.)

0.60044

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

mean = 544 and population standard deviation = 103

a) For x = 500

z = 500 - 544/103

z = -0.42718

Determining it's Probability value from Z-Table:

P(x≤ 500) = P(x = 500)= 0.33462

b) For x = 700

z = 700 - 544/103

z = 1.51456

P-value from Z-Table:

P(x ≤ 700) = P(x = 700) = 0.93506

Hence, the probability of applicants who score is between 500 and 700 is calculated as

P(x = 700) - P(x = 500)

P(z = 1.51456) - P(z = -0.42718)

= 0.93506 - 0.33462

= 0.60044

The probability of applicants who score is between 500 and 700 is 0.60044

kaahe btau