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Although bats are not known for their eyesight, they are able to locate prey (mainly insects)...

Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect. 23 40 27 56 52 34 42 61 68 45 83 (a) Compute the sample mean distance at which the bat first detects an insect. (Round your answer to three decimal places.) cm (b) Compute the sample variance and standard deviation for this data set. (Round your answers to two decimal places.) Variance?

Standard deviation?

Solutions

Expert Solution

Solution:

Given that,

23 40 27 56 52 34 42 61 68 45 83

n = 11

a )The mean of sample is   

x/n =  ( 23 + 40 + 27 + 56 + 52 + 34 + 42 + 61 + 68 + 45 + 83 / 11)

   = 531 / 11

= 48.273

The sample mean is 48.273

Sample variance is s2

s2 = 1/(n-1)(x - )2

=  1/11 - 1 (23 - 48.273 )2+ (40 - 48.273)2+ (27 - 48.273 )2+ (56 - 48.273 )2 +( 52 - 48.273)2 + ( 34 - 48.273)2 +(42 - 48.273)2 + (61 - 48.273)2 + (68 - 48.273)2 + (45 - 48.273)2 + (83 - 48.273)2

= 1/10 (638.724529 + 68.442529 + 452.540529 + 59.706529 + 13.890529 + 203.718529 + 39.350529 + 161.976529 + 389.154529 + 10.712529 + 1205.964529)

= 3244.181819/10

= 324.42

sample variance = s2 = 324.42

The sample standard deviation is = s = s2 = 324.42 = 18.01

milcah answered 1 year ago
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