"In Problems 23–32, assume that the random variable X is normally distributed, with mean μ = 50 and standard deviation σ = 7. Compute the following probabilities. Be sure to draw a normal curve with the area corresponding to the probability shaded.
P(55 ≤ X < 70)"

The normal distribution is a continuous probability distribution characterized by its symmetric, bell-shaped curve defined by the mean (μ) and standard deviation (σ). It models many natural phenomena and allows calculation of probabilities for ranges of values using the area under the curve.

Standardization converts a normal random variable X into a standard normal variable Z by subtracting the mean and dividing by the standard deviation: Z = (X - μ) / σ. This transformation allows use of standard normal tables to find probabilities for any normal distribution.

In a normal distribution, the probability that X falls within a certain interval corresponds to the area under the curve between those values. Calculating P(55 ≤ X < 70) involves finding the area under the normal curve between 55 and 70, often using Z-scores and standard normal tables.