Question

For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and want to know the probability that the length of time will be between 50 and 70 hours.

Entry to a certain University is determined by a national test.  The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100.  Jauna wants to be admitted to this university and she knows that she much score better than at least 70 % of the students who took the test.  Jauna takes the test and scores 585. Will she be admitted to this university?

The length of similar components produced by a company are approximated by a normal distribution model with a mean of 5 cm and a standard deviation of .02 cm.  If a component is chosen at random

 What is the probability that the length of this component is between 4.98 and 5.02 cm?

B. what is the probability that the length of this component is between 4.96 and 5.04 cm?

Answer 1

a)

b)

582>K, hence she ll be admitted to the University.

c)

Using Empirical formula,
The probability that the length of this component is between 4.98 and 5.02 cm is 0.68.

The probability that the length of this component is between 4.96 and 5.04 cm is 0.95.