The medical records of infants delivered at Kaiser Memorial Hospital show that the infants' lengths at birth (in inches) are normally distributed with a mean 25 and a standard deviation of 2.5. Find the probability that an infant selected at random from among those delivered at the hospital measures less than 19 in.
A) 0.1151
B) 0.0082
C) 0.8849
D) 0
E) 0.9918

Question

The medical records of infants delivered at Kaiser Memorial Hospital show that the infants' lengths at birth (in inches) are normally distributed with a mean 25 and a standard deviation of 2.5. Find the probability that an infant selected at random from among those delivered at the hospital measures less than 19 in. ​
A) 0.1151
B) 0.0082
C) 0.8849
D) 0
E) 0.9918

Quizplus · Accepted Answer

To find the probability that an infant measures less than 19 inches, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (19 inches), μ is the mean (25 inches), and σ is the standard deviation (2.5 inches). Plugging in the values, we get Z = (19 - 25) / 2.5 = -6 / 2.5 = -2.4. Looking up the Z-score of -2.4 in the standard normal distribution table gives a probability of approximately 0.0082.

The Medical Records of Infants Delivered at Kaiser Memorial Hospital