Question

Q1- If you know that the birth weights of male babies have a standard deviation of 1.33 lb.

Determine the percentage of all samples of 400 male babies that have mean birth weights within .

125 lb of the population mean birth weights of all male babies.

Answer 1

Let the mean birth weight of male babies population is .

Standard deviation is , = 1.33

Let X be a random variable denoting birth weights of a male babies.

n =400 .

So,from central limit theorem we know that mean of it will follow normal since n is very large

So, N( ,2/n) =N ( , 1.77/400)

Now, P ( -.125    +.125 ) = P ( ( -.125 - )/(/)   (- )/(/) ( +.125 - )/(/))

=P(-.125/(1.33/20) Z ​​​​​​​ .125/(1.33/20)) [converting to standard normal]

= P( -1.88   Z ​​​​​​​ 1.88)

= P (Z ​​​​​​​ 1.88) - P( Z ​​​​​​​ -1.88)

= - [ is distribution function for standard normal]

= - (1 -  )

=2 x   - 1

=2 x 0.96995 -1

= 0.9399

Probability that the mean birth weight is within .125 lb of the population mean birth weights of all male babies is , 0.9399 or 93.99 % .

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