Question

Bayou City Bolts distributes bolts with lengths that are normally distributed with a mean of 4 inches and a standard deviation of 0.007 inches. About 68 % of all bolts manufactured and distributed will be between what lengths? What percentage of bolts will be between 3.993 inches and 4.014 inches?

Answer 1

Solution :

Given that,

= 4

= 0.007

(A)Using Empirical rule,

P( - 1< X < + 1) = 68%

P(4 - 0.007 < X < 4 + 0.007) = 68%

P(3.993 < X < 4.007) = 68%

Answer = 3.993 nd 4.007

(B)

P(3.993< x <4.014) = P[(3.993 - 4) /0.007< (x - ) / < (4.014 - 4 ) /0.007 )]

= P( -1< Z < 2)

= P(Z <2)+P(Z <-1 )

using empirical rule

=95%/2 + 68%/2

=47.5%+34%

=81.5%