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TotCo is developing a new deluxe baby bassinet. If the length of a newborn baby is normally distributed with a mean of 50 cm and a standard deviation of 5 cm, what should be the interior length of the bassinet to ensure that 99 percent of newborn babies will fit, with a safety margin of 10 cm on each end of the bassinet

Respuesta :

Answer:

The interior length of the bassinet to ensure that 99 percent of newborn babies will fit   = 1.7 cm

Step-by-step explanation:

Explanation:-

step(i):-

Given mean of population = 50 cm  

standard deviation of Population = 5 cm

Given Margin of error = 10 cm

The Margin of error is determined by

[tex]M.E = \frac{Z_{\alpha } S.D}{\sqrt{n} }[/tex]

Step(ii):-

Given level of significance ∝ = 99 % or 1 %

Z₀.₀₁ = 2.576

[tex]10 = \frac{2.576 X 5}{\sqrt{n} }[/tex]

[tex]\sqrt{n} = \frac{2.576 X 5}{10}[/tex]

√n = 1.3

squaring on both sides , we get

n = 1.69≅ 1.7 cm

Final answer:-

The interior length of the bassinet to ensure that 99 percent of newborn babies will fit   = 1.7 cm

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