Question

The gestation period for cats has an approximate mean of 64 days and a standard deviation of 3 days, and the distribution of the gestation period has an approximate Normal distribution. What proportion of kittens are born between 61 and 67 days after conception?

The gestation period for cats has an approximate mean of 64 days and a standard deviation of 3 days and the distribution of the gestation period is approximately Normal. What proportion of kittens have a gestation period longer than 70 days?

Heights of young adult women in the United States are approximately Normal with a mean of 64 inches and standard deviation 2.7 inches. What proportion of all young adult women in the United States are taller than 6 feet?

Answer 1

1) Let X be the gestation period for cats

X~ Normal ( 64, 3)

P( 61 < X < 67) = P( < < )

= P( -1 < z < 1)

= P( z < 1) - P( z < -1)

= P( z < 1) - 1 + P( z < 1)

= 2P(z < 1) - 1

= 2*0.84134 - 1

= 0.68268

2) Let X be the gestation period for cats

X~ Normal ( 64, 3)

P( X > 70) = P( > )

= P( z > 2)

= 1- P( z < 2)

= 1- 0.97725

= 0.02275

3) Let X be the Heights of young adult women in the United States

X~ Normal ( 64, 2.7)

P( X > 6 feet) = P( X > 72 inch)

= P( > )

= P( z > 2.96)

= 1- P( z < 2.96)

= 1- 0.99846

= 0.00154

answered by: anonymous