Respuesta :
Answer:
91.63 cm is the interior length of the bassinet to ensure that 99 percent of newborn babies will fit, with a safety margin of 15 cm on each end of the bassinet.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50 cm
Standard Deviation, σ = 5 cm
We are given that the distribution of length of a newborn baby is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X<x) = 0.99
We have to find the value of x such that the probability is 0.99
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 50}{5})=0.99[/tex]
Calculation the value from standard normal table, we have,
[tex]P(z<2.326) = 0.99[/tex]
[tex]\displaystyle\frac{x - 50}{5} = 2.326\\x = 61.63[/tex]
Thus, 99% of newborn babies will have a length of 61.63 cm or less.
There is a safety margin of 15 cm on each end of the bassinet
Length of bassinet =
[tex]61+63 + 15 +15 = 91.63\text{ cm}[/tex]
