sam ask the students in his school to select their favorite sport. half of the students said their favorite sport was soccer. on
1 answer:
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Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
.
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X
Answer:
(b)
Step-by-step explanation:
1 male named Bart (b)
3 females named Charlene(c), Diana(d), and Erin(e).
Since there is replacement, the possible samples are:
bb, bc, be, bd, cb, cc, cd, ce, db, dc, dd, de, eb, ec, ed, and ee.
Total Number of pairs = 16
Event of picking 2 males:bb
Event of 1 male:bc,cb,bd,db,be,eb
Event of picking 0 males:
cc, cd, ce, dc, dd, de, ec, ed, and ee.
b. The mean of the sampling distribution
c. No; the proportion of males is while the mean is
.
B. No, the sample mean is not equal to the population proportion of males. These values are not always equal, because proportion is an unbiased estimator.