Question

The certain paper su technology.) with mean 3,500 grams and standard 510 grams is a One or mon med cal definition of a large baby is any baby that weighs more than 4,000-at birth. What is the probabilty that your answer to four decimal places.) a) randomly selected Canadian baby is』large baby7(Round (b) what is the probability that a randomly selected Canadian baby weighs either less than 2,000 grams or more than 4,000 grams at birth? (Round your answer to four decimal places) what birth weights describe the 25% of Canadian babies with the greatest Any baby with a weight of (c) birth wegres,(Round your answer to the nearest integer.) rams or more is in the ratest 2S% of bith weights.

Answer 1

Here we have $\mu$ = 3500, $\sigma$ = 510

a) Here we need to find

p ( x > 4000 )

$=p\left ( \frac{x-\mu }{\sigma }>\frac{4000-3500}{510} \right )$

= p ( z > 0.98 )
= 1 - p ( z $\leq$ 0.98 )

= 1 - 0.8365 ------( using excel formula " =norm.s.dist(0.98,1)" )

= 0.1635

b) Here we need to find

p ( x < 2000 or x > 4000 ) = p ( x < 2000) + p( x > 4000 )

p ( x < 2000 )

$=p\left ( \frac{x-\mu }{\sigma }<\frac{2000-3500}{510} \right )$

= p ( z < -2.94 )

= 0.0016 ------( using excel formula " =norm.s.dist(-2.94,1)" )

So,

p ( x < 2000 or x > 4000 ) = 0.0016 + 0.1635 = 0.1651

C) Here we have greatest 25%

p (Z > z) = 0.25

1 - p ( Z $\leq$ z ) = 0.25

p ( Z $\leq$ z ) = 1 - 0.25 = 0.75

So we get z = 0.67 --------- ( Using excel formula " =norm.s.inv(0.75)" )

$\frac{x -\mu }{\sigma }=0.67$

$\frac{x -3500 }{510 }=0.67$

x = 3841.7 $\approx$ 3842 gram

Any baby with weight of 3842 gram or more is in the greatest 25 % of birth weights.