Final answer:
To find the probabilities, use the standard normal distribution and calculate the corresponding z-scores. For Pr(X < 53), the probability is approximately 0.9332. For Pr(48 < X < 51), the probability is approximately 0.5328.
Step-by-step explanation:
To find the probabilities, we can use the standard normal distribution. We can convert the given values to z-scores using the formula z = (x - mean) / standard deviation.
a. Pr( X < 53 )
To find this probability, we need to calculate the z-score for X = 53. z = (53 - 50) / 2 = 1.5
Then, we can use a standard normal table or a calculator to find the probability corresponding to this z-score.
From the table or calculator, we find that the probability is approximately 0.9332.
Therefore, Pr( X < 53 ) = 0.9332
b. Pr( 48 < X < 51)
To find this probability, we need to calculate the z-scores for X = 48 and X = 51.
For X = 48, z = (48 - 50) / 2 = -1
For X = 51, z = (51 - 50) / 2 = 0.5
Then, we can use a standard normal table or a calculator to find the probabilities corresponding to these z-scores.
From the table or calculator, we find that the probability for z = -1 is approximately 0.1587 and the probability for z = 0.5 is approximately 0.6915.
Therefore, Pr(48 < X < 51) = 0.6915 - 0.1587 = 0.5328.