How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of ? = 25.9 ounces with a (95% of data) range from 16.4 to 35.4 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.) (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 14% 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.)
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
How much should a healthy kitten weigh? Suppose that a healthy 10-week-old (domestic) kitten should weigh an average of ? = 25.9 ounces with a (95% of data)
(a) The
For a symmetric, bell-shaped distribution,
| standard deviation ≈ |
|
≈ |
|
Estimate the standard deviation of the x distribution. (Round your answer to two decimal places.)
(b) What is the
(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 14% 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.)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
