Question

How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of ? = 22.9 ounces with a (95% of data) range from 13.4 to 32.4 ounces. Let x 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 ? ? 2? to ? + 2? is often used for "commonly occurring" data values. Note that the interval from ? ? 2? to ? + 2? is 4? 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,

standard deviation ?

range 4

?

high value ? low value 4

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 16% 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.)
oz

Answer 1

a) Since 95% of data range from 13.4 to 32.4 ounces. So

Hence

Define the standard random variable Z as

X is weight of 10-week old Kitten

a) Required probability is

b)

d)

e) Let X=a, be the cutoff then