Question

Length of metal strips produced by a machine process are normally distributed with a mean length of 250cm and a standard deviation of 20cm. Giving your answer as a decimal to 4 decimal places, find the probablility that the length of a randomly selected strip is Shorter than 214cm Submit part 1 mark Unanswered Longer than 294cm Submit part

Answer 1

Solution :

Given that ,

mean = $\mu$ = 250

standard deviation = $\sigma$ =20

P(x < 214 ) = P[(x - $\mu$ ) / $\sigma$ < (214-220) /20 ]

= P(z < -0.30 )

= 0.0013

probability =0.0013

b)

P(x > 294) = 1 - p( x< 294 )

=1- p [(x - $\mu$ ) / $\sigma$ < (294-220) /20 ]

=1- P(z < 3.7)

= 1 - 0.9999 = 0.0001

probability = 0.0001

c)

P( 200< x < 290) = P[(200-220)/20 ) < (x - $\mu$ ) /$\sigma$  < (290-220) /20 ) ]

= P(-1 < z < 3.5 )

= P(z < 3.5) - P(z < -1 )

Using standard normal table

= 0.9998- 0.1587 = 0.8411

Probability = 0.8411