Question

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The weights of newborn children in the U.S. vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds. a) What is the probability that a baby chosen at random weighs less than 5.5 pounds at birth? b) You choose 10 babies at random. What is the probability that their average birth weight is less than 5.5 pounds?

Answer 1

Solution :

Given that ,

a) P(x < 5.5)

= P[(x - $\mu$ ) / $\sigma$ < (5.5 - 7.5) / 1.25]

= P(z < - 1.6)

Using z table,

= 0.0548

b) $\mu$ _{$\bar x$} = 7.5

$\sigma$ _{$\bar x$} = $\sigma$ / $\sqrt$ n = 1.25 / $\sqrt$ 10 = 0.40

P( $\bar x$ < 5.5 ) = P(( $\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (5.5 - 7.5) / 0.40)

= P(z < - 5)

Using z table

= 0