Question

Weights of 10-ounce bag corn chips follow a normal distribution with µ=10 and σ=0.3 ounces. Find the probability that

–(i) the sample mean weight of 49 randomly selected bags exceeds 10.25 ounces.

–(ii) the sample mean weight of 49 randomly selected bags is less than 10.20 ounces.

Answer 1

Solution :

Given that ,

mean = = 10

standard deviation = = 0.3

n = 49

= 10 and

= / n = 0.3 / 49 = 0.3 / 7

(i)

P( > 10.25) = 1 - P( < 10.25)

= 1 - P(( - ) / < (10.25 - 10) / 0.3 / 7 )

= 1 - P(z < 5.83)

    Using standard normal table,

P( > 10.25) = 1 - 1 = 0

Probability = 0

(ii)

P( < 10.20) = P(( - ) / < (10.20 - 10) / 0.3 / 7)

= P(z < 4.67)

Using standard normal table,

P( < 10.20) = 1

Probability = 1

= 0.3 or 3 ??