91Ó°ÊÓ

To calculate the probability of newborn hippos weighing between 90 and 110 pounds, first we normalize our required range by finding the respective z-scores. \nThe z-score equation is \(Z = (X - μ) / σ\), where X is the value we want to normalize, μ is the mean, and σ is the standard deviation. For the lower range (90 pounds): \(Z1 = (90 - 88) / 10 = 0.2\), and for the upper range (110 pounds): \(Z2 = (110 - 88) / 10 = 2.2\). \nNext, we look up these z-scores on the z-table to find the corresponding probabilities. For Z1, the area to the left under the normal curve corresponds to a probability of 0.5793 and for Z2, the probability is 0.9861. \nTo find the probability that a newborn hippo weights between 90 and 110 pounds, subtract the lower probability from the higher one: 0.9861 - 0.5793 = 0.4068, which translates to a 40.68% chance.

To find the weight that corresponds with the 5th percentile for newborn hippos, we first need to find the corresponding z-score from the table for 5th percentile, which is -1.645. \nThen, we use this z-score to find the corresponding real value in pounds using the inverse of the z-score equation: \(X = Z * σ + μ\), where Z is the z-score, σ is the standard deviation, and μ is the mean. Here, \(X = -1.645 * 10 + 88 = 72.55\) pounds. So, newborn hippos with weights at or below this are unlikely to survive.

To find the percentage of hippos born weighing 29 pounds or less, calculate the z-score for 29 pounds using the z-score equation: \(Z = (29 - 88) / 10 = -5.9\). \nLook up this z-score on the z-table, but since this is off the chart (the z-table typically goes down to -3.49 only), we can conclude that almost no baby hippo will be born at this weight. Therefore, the percentage is virtually 0%.