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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

Mating calls The durations of the mating calls of a population of tree toads are normally distributed, with mean 189 milliseconds (msec) and standard deviation 32 msec. What proportion of these calls would be expected to last between

(a) 157 and 221 msec? (b) 205 and 253 msec?

(a)

To determine

To calculate: The probability that a call would last between 157 and 221 milliseconds using standard normal distribution if suppose the duration of the mating calls of a population of tree toads are normally distributed with a mean of 189 milliseconds and a standard deviation of 32 msec.

Explanation

Given Information:

The probability that a call would last between 157 and 221 milliseconds, so the probability is Pr(157x221).

The mean is 189 milliseconds and a standard deviation is 32 msec.

Formula used:

If data for a population are normally distributed, the z score is,

z=xμσ

Where σ is the standard deviation of the population data, x is the number of standard deviation and μ is mean.

Calculation:

Consider the provided probability is Pr(157x221),

The mean is μ=189 and a standard deviation is σ=32.

To find the value of provided probability use the formula z=xμσ.

So the probability Pr(157x221) will convert into:

Pr(15718932xμσ22118932)=Pr(<

(b)

To determine

To calculate: The probability that a call would last between 205 and 253 milliseconds using standard normal distribution if suppose the duration of the mating calls of a population of tree toads are normally distributed with a mean of 189 milliseconds and a standard deviation of 32 msec.

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