Then standardize the two scores
48 and 52
to be able to consult the table.
The formula for changing a raw score x into a z score is
Z=X−μσ.
For this problem, X is normal with
μ=50 and σ=5.
So, by symmetry of the standard normal curve,
P(48<X<52)
=P(48−50<X−50<52−50)
=P(48−505<X−505<52−505)
=P(−25<Z<25)
=P(−.40<Z<.40)
=P(Z<.40)−P(Z<−.40)
=P(Z<.40)−P(Z>.40)
=P(Z<.40)−(1−P(Z<.40))
=2P(Z<.40)−1
=2(.6554)−1
=1.3108−1
=.3108≈.31
=31%.
