Question

A machine producing vitamin E capsules operates so that the actual amount of vitamin E in each capsule is normally distributed with a mean of 4 mg and a standard deviation of 0.05 mg. Let x = the actual amount of vitamin E in a randomly selected capsule. (Round your answers to four decimal places.) What is the probability that a randomly selected capsule contains less than 3.95 mg of vitamin E? What is the probability that a randomly selected capsule contains at least 4.25 mg of vitamin E? You may need to use the appropriate table in the appendix or technology to answer this question.

Answer 1

Solution :

Given that ,

mean = = 4

standard deviation = = 0.05

a) P(x < 3.95) = P[(x - ) / < (3.95 - 4) / 0.05 ]

= P(z < -1)

Using z table,

= 0.1587

b) P(x 4.25) = 1 - P(x   4.25)

= 1 - P[(x - ) / ( 4.25 - 4 ) / 0.05]

= 1 -  P(z 5)   

  Using z table,

= 1 - 1

= 0