STAT 205 Quiz: STAT 205 South Carolina Quiz5 key
NAME:
Stat 205 Quiz 5
The heights of a certain population of corn plants follow a normal distribution with mean
µY= 145 cm and standard deviation σY= 22 cm.
(a) (4 points) What percentage of plants are between 140 cm and 150 cm tall?
Answer: This is
P(140 ≤Yi≤150) = Pµ140 −145
22 ≤Yi−145
22 ≤150 −145
22 ¶
=P(−0.227 ≤Z≤0.227)
≈P(Z≤0.23) −P(Z≤ −0.23)
= 0.59 −0.41
= 0.18.
Also: normalcdf(140,150,145,22).
(b) (4 points) Let ¯
Ybe the mean height of a random sample of n= 16 plants from the
population. What is P(140 ≤¯
Y≤150)?
Answer:
P(140 ≤¯
Y≤150) = Pµ140 −145
22/√16 ≤Yi−145
22/√16 ≤150 −145
22/√16 ¶
=P(−0.91 ≤Z≤0.91)
≈P(Z≤0.91) −P(Z≤ −0.91)
= 0.82 −0.18
= 0.64.
Also: normalcdf(140,150,145,5.5).
(c) (4 points) What is P(¯
Y≤145) = P(¯
Y≤µY)?
Answer: 0.5.
