How much should a healthy kitten weigh? Suppose that a healthy 10-week—old (domestic) kitten should weigh an average ofu = 23.7 ounces with a (95% of data) range from

13.0 to 34.4 ounces. Letx be a random variable that represents the weight (in ounces) of a healthy 10-week—old kitten. Assume that x has a distribution that is approximately

normal. (a) The empirical rule (Section 7.1) indicates that for a symmetrical and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of

the mean. Therefore, a 95% range of data values extending from p — 20 to p + 20 is often used for "commonly occurring" data values. Note that the interval from

p — 20 to p + 20 is 40 in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviation For a symmetric, bell-shaped distribution, range high value — low value

5 — 4 4 standard deviation = where it is estimated that about 95% of the commonly occurring data values fall into

this range. Estimate the standard deviation of the x distribution. (Round your answer to two decimal places.)

oz (b) What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces? (Round your answer to four decimal places.) (c) What is the probability that a healthy 10-week—old kitten will weigh more than 33 ounces? (Round your answer to four decimal places.) (d) What is the probability that a healthy 10-week-old kitten will weigh between 14 and 33 ounces? (Round your answer to four decimal places.) (e) A kitten whose weight is in the bottom 11% of the probability distribution of weights is called undernourished. What is the cutoff point for the weight of an

undernourished kitten? (Round your answer to two decimal places.) 02