Question

Please help with BOTH of these questions!!! Thank you!!

After taking an aptitude test, the computer told Bob that he had a z-score of 1.08. If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select all that apply. Select one or more: Bob scored within 2 standard deviations of the mean score. Bob did better than the mean score. Bob scored within 1 standard deviation of the mean score. Bob did worse than the mean score. About 14% of students taking the aptitude test did better than Bob. About 14% of students taking the aptitude test did worse than Bob. The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of highs risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. What proportion of children have MDI of at least 807 Select one: 0.8944 0.7881 02119 0.1056

Answer 1

1.

z-score = 1.08

Mean score = 0

Std. deviation = 1

So, Interval for scores within of 2 std. deviation of mean = [-1, 1]

p-value of z = 0.140071

Based on the above facts following statements are true:

A. Bob scored within 2 Std. deviation of mean score

B. Bob score better than the mean score

E. About 14% of the students taking the score did better than Bob

2.

MDI ~ $\fn_phv N(100, 16^{2})$

So,

For MDI = 80

Z = (80-100)/16

= -1.25

P(Z>=-1.25) = 0.89435