You need to define your question better. X by itself is usually just

the probability of one sample. The term X with a bar on top of it is often

used to mean the distribution of the sample mean. You must want the distribution of the sample

mean, but you did not say so.

Do you want the probability that the sample mean is 94 < x< 94.5

P( 94< X_bar< 94.5) = P(X<94.5) - P(X< 94)

sigma_sample_mean = Sigma_population/sqrt(N)= 10/sqrt(4) = 10/2 =5

P(X_bar< 94.5) = P( Z < (x-mean)/ sigma_sample_mean)

P(X_bar< 94.5) = P(Z< (94.5 -103)/ 5 )= P(Z< (-7.5/5) ) = P(Z< -1.5)

Using this online table:

https://www.stat.tamu.edu/~lzhou/stat302/standardn...

P(X_bar< 94.5) = P(Z< -1.5) = .06681

P(X_bar< 94) = P( Z< (94-103)/5) = P( Z < -8/5)

P(X_bar< 94) = P(Z < -1.6) = .05480

P( 94< X_bar< 94.5) = P(X<94.5) - P(X< 94)

P( 94< X_bar< 94.5) = +0.06681-0.05480 = 0.01201

=== answer

P(94< X_bar < 94.5 ) = 0.01201

If you didn't want the distribution of the sample mean, you would need to define

what you want. For example, the probability that 2 out of the 4 samples are in this

region or the probability that 3 of 4 samples are in this region.