Question

Question 3:

a.) A manufacturer knows that their items have a normally distributed length, with a mean of 19.6 inches, and standard deviation of 2.4 inches.

If 4 items are chosen at random, what is the probability that their mean length is less than 17.5 inches?

b.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.5 years, and standard deviation of 0.7 years.

If you randomly purchase 14 items, what is the probability that their mean life will be longer than 8 years?

c.) A particular fruit's weights are normally distributed, with a mean of 561 grams and a standard deviation of 15 grams.

If you pick 5 fruit at random, what is the probability that their mean weight will be between 544 grams and 560 grams

Answer 1

Solution, Given that xu Normal distribution with u = 19.6 6 = 2.4, n = 4 Here, ux = 1=19.6 67 2.4 1.2 va p( is less than 17.5) E P ( x < 17.5) (x-uk < 17.5-1916) E plz <-2.1) (using a table) 6 1.2 0.0179 . Given that x n Normal distribution with u = 7.5 8 = 0.7, n = 14 Here, lux = u = 7,5 0.7 0.18 P(x is longee than 8) P(x > 8) 8- 7.5 0.18 - P(Z > 2.78) 1-P(Z < 2.78) - 0.9973 0.0027 1 (using a table) (construm

n=5 15 ® Given that x n Normal distribution with U = 561, 0 = 15, Hece, x = l = 561 - 6.70 15 - P(x is between 544 and 560) p( x < 560) - P(x < 544) 560-561 poslu 61) - X-l < 544-561 Ox 67 6.70 6.70 - P(Z <-0.15) - P(Z <-2.54) O.4404 0.0055 (using z table) 0.4349 561)