Can someone help me with this question?
2 answers:
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Answer:
The last guy's height is 69 inches
Step-by-step explanation:
mean=sum of all numbers/number of numbers
There are 5 numbers in the set which means that 65 is the sum of all five numbers divided by 5. To reverse that we multiply 65 by 5 to get the sum of all of the numbers.
325 is the sum of all of the numbers so to find the missing number you add up all of the known numbers in the set and find the difference between that sum and 325.
The missing guy's height is 69 inches.
Answer:
a)
<em>The probability that a single score drawn at random will be greater than 110 </em>
<em>P( X > 110) = 0.1587</em>
<em>b) </em>
<em>The probability that a sample of 25 scores will have a mean greater than 105</em>
<em> P( x> 105) = 0.0062</em>
<em>c) </em>
<em>The probability that a sample of 64 scores will have a mean greater than 105</em>
<em> P( x⁻> 105) = 0.002</em>
<em></em>
<em>d) </em>
<em> The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105</em>
<em> P( 95 ≤ X≤ 105) = 0.9544</em>
<em></em>
Step-by-step explanation:
<u><em>a)</em></u>
Given mean of the Normal distribution 'μ' = 100
Given standard deviation of the Normal distribution 'σ' = 10
a)
Let 'X' be the random variable of the Normal distribution
let 'X' = 110
<em>The probability that a single score drawn at random will be greater than 110</em>
<em>P( X > 110) = P( Z >1)</em>
= 1 - P( Z < 1)
= 1 - ( 0.5 +A(1))
= 0.5 - A(1)
= 0.5 -0.3413
= 0.1587
b)
let 'X' = 105
<em>The probability that a single score drawn at random will be greater than 110</em>
<em> P( x> 105) = P( z > 2.5)</em>
<em> = 1 - P( Z< 2.5)</em>
<em> = 1 - ( 0.5 + A( 2.5))</em>
<em> = 0.5 - A ( 2.5)</em>
<em> = 0.5 - 0.4938</em>
<em> = 0.0062</em>
<em>The probability that a single score drawn at random will be greater than 105</em>
<em> P( x> 105) = 0.0062</em>
<em>c) </em>
let 'X' = 105
<em>The probability that a single score drawn at random will have a mean greater than 105</em>
<em> P( x> 105) = P( z > 4)</em>
<em> = 1 - P( Z< 4)</em>
<em> = 1 - ( 0.5 + A( 4))</em>
<em> = 0.5 - A ( 4)</em>
<em> = 0.5 - 0.498</em>
<em> = 0.002</em>
<em> The probability that a sample of 64 scores will have a mean greater than 105</em>
<em> P( x⁻> 105) = 0.002</em>
<em>d) </em>
<em>Let x₁ = 95</em>
<em>Let x₂ = 105</em>
The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105
P( 95 ≤ X≤ 105) = P( -2≤z≤2)
= P(z≤2) - P(z≤-2)
= 0.5 + A( 2) - ( 0.5 - A( -2))
= A( 2) + A(-2) (∵A(-2) =A(2)
= A( 2) + A(2)
= 2 × A(2)
= 2×0.4772
= 0.9544
<em> The probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105</em>
<em> P( 95 ≤ X≤ 105) = 0.9544</em>
<em> </em>