B. The mean score of the students in the science Quiz given by Miss Reyes is 35 with a standard deviation of
12. What is the probability that randomly selected students will have the following score:
a. Below 30
Since µ=35 and σ= 12,
P(X<30) = P(𝑍 <
𝑋−µ
)
σ
30−35
)
12
=(
=-0.42
Use standard normal table to conclude that:
P(Z< -0.42)= 0.33724
b. Above 45
Since µ=35 and σ= 12,
P(X>45) = P(𝑍 <
𝑋−µ
)
σ
P(X>45) = 𝑃(𝑍 <
45−35
)
12
=P(Z>.83)
Use the standard normal table to conclude that:
P(Z<.83) = 1-0.79673
P(Z<.83) = 0.20327
c. Below 50
Since µ=35 and σ= 12
P(X<50) = P(𝑍 <
𝑋−µ
)
σ
P(X<50) = 𝑃(𝑍 <
50−35
)
12
=1.25
Use the standard normal table to conclude that:
P(Z<1.25) = 0.89435
d. Above 20
Since µ=35 and σ= 12
P(X>20) = P(𝑍 <
𝑋−µ
)
σ
P(X>20) = 𝑃(𝑍 <
20−35
)
12
=-1.25
Use the standard normal table to conclude that:
P(Z>-1.25) =0.89435
e. Between 10 and 60
Since µ=35 and σ= 12
10−µ
σ
P(10<X<60) = P (
<
𝑋−µ
σ
<
60−µ
)
σ
=P (-2.08 < Z <2.08)
Use the standard normal table to conclude that:
P (-2.08 < Z <2.08) =0.98124-0.01876
= 0.96248
f. Between 40 and 55
Since µ=35 and σ= 12
40−µ
σ
P(40<X<55) = P(
<
𝑋−µ
σ
<
55−µ
)
σ
=P (0.42 < Z < 1.67)
Use the standard normal table to conclude that:
P (0.42 < Z < 1.67) = 0.95254-.066276
=0.28978
g. Between 15 and 30
Since µ=35 and σ= 12
15−µ
σ
P(15<X<30) = P (
<
𝑋−µ
σ
<
30−µ
)
σ
=P (-0.42 < Z < -1.67)
Use the standard normal table to conclude that:
P (-0.42 < Z < -1.67) = 0.33724 – 0.04746
= 0.28978