Final answer:
To calculate the probability that a randomly selected student will be taller than 71 inches in an all boys school with a normal distribution of heights and a mean of 70 inches and a standard deviation of 3 inches, we need to convert the height into a z-score and find the area under the standard normal curve to the right of that z-score.
Step-by-step explanation:
Step 1: Define the problem
We have a normally distributed data set with a mean of 70 inches and a standard deviation of 3 inches.
Step 2: Convert the problem to a standard normal distribution
To calculate the probability, we need to convert the height value of 71 inches into a z-score using the formula: z = (x - μ) / σ. Plugging in the values, we get z = (71 - 70) / 3 = 0.3333.
Step 3: Find the probability
To find the probability of selecting a student taller than 71 inches, we need to find the area under the standard normal curve to the right of the z-score.
Using a Z-table or a calculator, we can find that the probability is approximately 0.3693.