Answer:
a. <u>0.5 or 50%</u>
b. <u>0.496 or 49.6%</u>
c. <u>0.8185 or 81.85%</u>
d. <u>Yes, it would be just 0.0013 or 0.13% of probability to find a typist whose speed exceeds 105 wpm</u>
e. <u>0.0252 or 2.52%</u>
f. <u>The qualifying speed would be 47.4 wpm.</u>
Step-by-step explanation:
a. Let's find the z-score this way:
μ = 60 σ= 15
z-score = (x - μ)/σ
z-score = (60 - 60)/15
z-score = 0
Now, let's calculate the p value for z-score = 0, using the z-table:
<u>p (z=0) = 0.5 or 50%</u>
b. z-score = (x - μ)/σ
z-score = (59.9 - 60)/15
z-score = -0.01
Now, let's calculate the p value for z-score = -.0.01, using the z-table:
<u>p (z = -0.01) = 0.496 or 49.6%</u>
If the question were less or equal than 60, a and b would have the same answer. But in this case, the question is "less than 60 wpm".
c.
z-score = (x - μ)/σ
z-score = (45 - 60)/15
z-score = - 1
Now, let's calculate the p value for z-score = -1, using the z-table:
p (z = -1) = 0.1587
z-score = (x - μ)/σ
z-score = (90 - 60)/15
z-score = 2
Now, let's calculate the p value for z-score = 2, using the z-table:
p (z = 2) = 0.9772
<u>In consequence,</u>
<u>p (-1 ≤ z ≤ 2) = 0.9772 - 0.1587 = 0.8185 or 81.85%</u>
d. z-score = (x - μ)/σ
z-score = (105 - 60)/15
z-score = 3
Now, let's calculate the p value for z-score = 3, using the z-table:
p (z = 3) = 0.9987
In consequence,
p (z > 3) = 1 - 0.9987 = 0.0013
<u>Yes, it would be just a 0.13% of probability to find a typist whose speed exceeds 105 wpm.</u>
e. z-score = (x - μ)/σ
z-score = (75 - 60)/15
z-score = 1
Now, let's calculate the p value for z-score = 1, using the z-table:
p (z = 1) = 0.8413
In consequence,
p (z > 1) = 1 - 0.8413 = 0.1587
and if the two typists are independently selected, then
p = 0.1587 * 0.1587
<u>p = 0.0252 or 2.52%</u>
f. p = 0.2, using the z-table, the z-score is -0.84, then:
z-score = (x - μ)/σ
-0.84 = (x - 60)/15
-12.6 = x - 60
-x = -60 + 12.6
-x = - 47.4
x = 47.4
<u>The qualifying speed would be 47.4 wpm.</u>
increases, [y] is expected to increase.