You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confide
1 answer:
Answer:
90% confidence interval, (109.47,116.53)
For 95% confidence interval (108.79,117.21)
Step-by-step explanation:
n =50
mean = 113
standard deviation = 15.20
a.) For 90% confidence interval, z=1.645
90% confidence interval is
=(113 - 3.53, 113 + 3.53)
=(109.47,116.53)
b.)For 95% confidence interval, z = 1.96
95% confidence interval is
=(113 - 4.21, 113 + 4.21)
=(108.79,117.21)
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Step-by-step explanation:
The upstream speed is S / t₁, and the downstream speed is S / t₂.
If we say f is the speed of the fish in calm water, and r is the speed of the river, then:
f − r = S / t₁
f + r = S / t₂
If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.
Using Pythagorean theorem:
f² = (ℓ/T)² + r²
f² − r² = (ℓ/T)²
(f − r) (f + r) = (ℓ/T)²
(S / t₁) (S / t₂) = (ℓ/T)²
S² / (t₁ t₂) = (ℓ/T)²
(t₁ t₂) / S² = (T/ℓ)²
√(t₁ t₂) / S = T/ℓ
T = ℓ√(t₁ t₂) / S
by using the integration formula
we get,
now put the value of t=\sin\theta in the above equation
we get,
hence proved