Answer :
P(120 < X < 153) is approximately 0.6025.
To calculate the probability, we need to find the area under the normal distribution curve between the two given values: 120 and 153.
Step 1: Standardize the values
To do this, we use the formula: Z = (X - μ) / σ
where X is the value, μ is the mean, and σ is the standard deviation.
For 120:
Z = (120 - 147) / 16 = -27 / 16 = -1.6875
For 153:
Z = (153 - 147) / 16 = 6 / 16 = 0.375
Step 2: Look up the probabilities
We can use a standard normal distribution table or calculator to find the probabilities associated with the standardized values.
P(120 < X < 153) = P(-1.6875 < Z < 0.375)
Using a standard normal distribution table or calculator, we find:
P(Z < -1.6875) = 0.0455 (rounded to four decimal places)
P(Z < 0.375) = 0.6480 (rounded to four decimal places)
Step 3: Calculate the probability
To find the probability between the two values, we subtract the smaller probability from the larger one.
P(120 < X < 153) = P(Z < 0.375) - P(Z < -1.6875)
= 0.6480 - 0.0455
= 0.6025
Rounding to four decimal places, the probability is approximately 0.6025.
Learn more about probability
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