Question

The weight, X, of cherry tomatoes selected at random from a very large bin at the local supermarket follows a Normal distribution with mean 3 oz. and standard deviation 2 oz. Suppose we pick 8 cherry tomatoes from the bin at random (independently) and put them in our bag. What is the probability that exactly 5 of the 8 cherry tomatoes weigh less than 4 oz (rounded to the nearest 0.01)?

Answer 1

Answer: the probability that exactly 5 of the 8 cherry tomatoes weigh less than 4 oz is 0.05

Explanation:

Given that;

X has normal distribution has mean µ = 3

standard deviation σ = 2

now

P( x< 4) = P( (x-µ)/σ /(3-4)/5)

= P( z < -0.5 )

= 0.3085 {from the z-table}

X has binomial distribution with n = 8 and p = 0.3085

so P(x=5)

P(x=5) = 8C₅(0.3085)⁵ (1 - 0.3085)⁸⁻⁵

= 0.0517 ≈ 0.05

Therefore the probability that exactly 5 of the 8 cherry tomatoes weigh less than 4 oz is 0.05