Question

5. The weights of the bowls of ramen that Naruto Uzumaki orders at Ichiraku’s are normally distributed with a mean of 2300 grams and a standard deviation of 500 grams.

a) What is the probability that a randomly selected bowl of ramen weighs at least 2475 grams?

b) What is the probability that a randomly selected bowl of ramen weighs between 2215 grams and 2390 grams?

c) What is the probability that a random sample of 25 bowls of ramen would result in a mean weight of no more than 2450 grams?

Answer 1

Solution :

Given that ,

a) P(x > 2475 ) = 1 - p( x< 2475 )

=1- p P[(x - ) / < (2475 - 2300) / 500]

=1- P(z < 0.35 )

= 1 - 0.6368

= 0.3632

b) P(2215 < x < 2390 ) = P[(2215 - 2300) / 500) < (x - ) /  < (2390 - 2300) / 500) ]

= P( - 0.17 < z < 0.18 )

= P(z < 0.18) - P(z < - 0.17)

Using z table,

= 0.5714 - 0.4325

= 0.1389

c) = 25

= / n = 500 / 25 = 100

P( < 2450) = P(( - ) / < (2450 - 2300) / 100)

= P(z < 1.5)

Using z table

= 0.9332