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3 years ago

Find the least whole number N so that 2020 + N is exactly divisible by 11.

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

8 0

2020 + N ≡ 0 (mod 11)

N ≡ -2020 (mod 11)

Notice that 2020 = 183 • 11 + 7, so

N ≡ -(183 • 11 + 7) (mod 11)

N ≡ -7 (mod 11)

N ≡ 4 (mod 11)

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90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

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Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

$se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }$

$se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }$

$se(x^{-} _{1} -x^{-} _{2} ) = 5.093$

Degrees of freedom

ν = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

$(x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})$

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

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