Transcript Using the Normal Distribution

Using the
Normal Distribution
Using the Normal Distribution tables calculate the
area under the standard normal curve for each of
the following
1.
P(Z < -0.58)
0.5-0.2190 = 0.2810
-0.58
0
0.4896-0.4525 = 0.0371
2.
P(-2.31 < Z < -1.67)
-2.31
3.
4.
P(Z > -1.871)
-1.67
0
-1.871
0
0.5+0.4694 = 0.9694
P(-1.5 < Z < 1.5)
0.4332+0.4332 = 0.8664
-1.5
5.
P(Z > -0.596)
0
0.5+0.2245 = 0.7245
0
6.
P(-1.97 < Z < 0.425)
0.4756+0.1646 = 0.6402
0
1.5
The mean mark in a university stage one math exam was
51% with a standard deviation of 16%.
Assuming the marks are normally distributed find the
probability that a student selected at random scored
1.
2.
Less than 55%
If 250 students sat the math exam how many scored between 35 and
45%?
X 
To standardise we use Z =

51 55
1.
To find
P(X < 55)
standardising
= P(Z <
Simplifying
= P(Z < 0.25)
Using tables
= 0.5 + 0.0987
= 0.5987
55  51
)
16
0 0.25
The mean mark in a university stage one math exam was
51% with a standard deviation of 16%.
Assuming the marks are normally distributed find the
probability that a student selected at random scored
1.
If 250 students sat the math exam how many scored between 35 and
45%?
To find
P(35 < X < 45)
standardising
= P(
Simplifying
= P(-1 < Z < -0.375)
Using tables
= 0.3413 - 0.1462
= 0.19517
Number of students
= 0.19517 x 250
= 48 students (rounding down)
55
35 -51
55 < Z < 45 -51
)
16
16
35 45 51
-1 0
-0.375