Question

examination grades in an introductory statistics course is normally distributed, with a mean of 75 and a standard deviation of 7. Complete parts (a) through (d) a. What is the probablity that a student scored below 87 on this exam? The probability that a shudent scored below 87 is (Round to four decimal places as needed.) b What is the probability that a student scored between 68 and 94 The probability that a student soored between 68 and 94 is (Round to four decimal places as needed) e. The probabity is 5% that a student taking the test scores higher than what gade? The probablity is 5% rat a student taking the test sores higher than Round to the nearest inbeger as needed) d if the polessor grades on a curve for example, teprofessor could give A's tote op10% of the Class, re an essoftho score is a sudent beter c" w th a grade of 89 n"าร e amoragrade 0,71onadno ere exam, where the mean is 68 and the standard deviation is 3? Show your answer statistically and explain A student is Round to two decimal places as needed.) with a grade of 89 on this exam because the Z value for the grade of 89 and the Z value for the grade of 71 is

Answer 1

Solution:- Given that mean = 75 and standard deviation = 7

a. P(X < 87) = P((X-μ)/σ < (87-75)/7)
= P(Z < 1.7143)
= 0.9564

b. P(68 < X < 94) = P((68-75)/7 < (X-μ)/σ < (94-75)/7)
= P(-1 < Z < 2.7143)
= 0.8379

c. Z = 1.645

X = μ + Z*σ = 75 + 1.645*7 = 86.515 = 87

d.

=> Z = (89-75)/7 = 2

Z = (71-75)/2 = -0.57