Concept explainers
Estimating the Standard Deviation: Veterinary Science How much should a healthy kitten weigh? A healthy 10-week-old (domestic) kitten should weigh an average of
(a) Estimate the standard deviation of the x distribution. Hint: See Problem 31.
(b) What is the probability that a healthy 10-week-old kitten will weigh less than 14 ounces?
(c) What is the probability that a healthy 10-week-old kitten will weigh more than 33 ounces?
(d) What is the probability that a healthy 10-week-old kitten will weigh between 14 and 33 ounces?
(e) Inverse
(a)
The standard deviation of x values using rule of thumb.
Answer to Problem 34P
Solution:
The standard deviation of x values using rule of thumb is 5.25.
Explanation of Solution
According to the rule of thumb for estimating the standard deviation from 95% range of data values is:
The standard deviation of x values using rule of thumb is 5.25.
(b)
The probability that a healthy 10 week old kitten will weigh less than 14 ounces.
Answer to Problem 34P
Solution:
The probability that a healthy 10 week old kitten will weigh less than 14 ounces is 0.0228.
Explanation of Solution
We have normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix
The probability that a healthy 10 week old kitten will weigh less than 14 ounces is 0.0228.
(c)
The probability that a healthy 10 week old kitten will weigh more than 33 ounces.
Answer to Problem 34P
Solution:
The probability that a healthy 10 week old kitten will weigh more than 33 ounces is 0.0526.
Explanation of Solution
We have normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix
The probability that a healthy 10 week old kitten will weigh more than 33 ounces is 0.0526.
(d)
The probability that a healthy 10 week old kitten will weigh between 14 and 33 ounces.
Answer to Problem 34P
Solution:
The probability that a healthy 10 week old kitten will weigh between 14 and 33 ounces is 0.9246.
Explanation of Solution
We have normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix
The probability that a healthy 10 week old kitten will weigh between 14 and 33 ounces is 0.9246.
(e)
The cutoff point for the weight of an undernourished kitten.
Answer to Problem 34P
Solution:
The cutoff point for the weight of an undernourished kitten is 17.8 ounces.
Explanation of Solution
We have normal distribution with
A kitten whose weight is in the bottom 10% of the probability distribution of weights is called undernourished.
From above we have
Area left of z = 0.10
By using Table 3 from appendix
By using formula for normal distribution:-
The cutoff point for the weight of an undernourished kitten is 17.8 ounces.
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