Question

Test scores on a Spanish language proficiency exam given to entering first year students at a certain university have a mean score of 78 with a standard deviation of 9 points (out of 100 points possible). Question 3 Subquestions 3.a 1 point(s) Suppose a first year student who took this Spanish proficiency exam is selected at random. What can be said about the probability that their score will be at least 80 points? 0.5871 0.0582 0.4129 0.9418 It cannot be determined accurately from the information given. Saved 3.b 1 point(s) Suppose a random sample of 50 first year students who took this Spanish placement exam will be selected, each of their scores are recorded, and the sample mean score out of 100 points will be computed. What can be said about the probability that the sample mean Spanish proficiency score will be at least 80? 0.5871 0.0582 0.4129 0.9418 It cannot be determined accurately from the information given. 3.c 1 point(s) Suppose computing the data for 50 students took too much time, and a random sample of a smaller size was taken such that the Central Limit Theorem would still apply. Describe how this change in sample size would have affected the following, if at all: The mean of the distribution for the sample mean Spanish placement exam score for a first year student at this university would ___________. Increase Decrease Remain unchanged Insufficient information to tell what would happen 3.d 1 point(s) Suppose computing the data for 50 students took too much time, and a random sample of a smaller size was taken such that the Central Limit Theorem would still apply. Describe how this change in sample size would have affected the following, if at all: The standard deviation of the distribution for the sample mean Spanish placement exam score for a first year student at this university would ___________. Increase Decrease Remain unchanged Insufficient information to tell what would happen 3.e 1 point(s) Suppose computing the data for 50 students took too much time, and a random sample of a smaller size was taken such that the Central Limit Theorem would still apply. Describe how this change in sample size would have affected the following, if at all: The probability that the sample mean Spanish proficiency score will be at least 80 would _____________. Increase Decrease Remain unchanged Insufficient information to tell what would happen

Answer 1

mean = 78 and sd = 9

a)
P(X > 80)
= P(z > (80 - 78)/9)
= P(z > 0.2222)
= 0.4121

Ans: 0.4129

b)
P(X > 80)
= P(z > (80 - 78)/(9/sqrt(50)))
= P(z > 1.5713)
= 0.0581

Ans: 0.0582

c)
The mean of the distribution for the sample mean Spanish placement exam score for a first year student at this university would Remain unchanged

d)
The standard deviation of the distribution for the sample mean Spanish placement exam score for a first year student at this university would increase

e)
The probability that the sample mean Spanish proficiency score will be at least 80 would increase