Question

The amount of ground coffee in a can from a particular production line is normally distributed with a mean of 200 grams and a standard deviation of 33 grams. If we select a random sample of 36 cans, the probability that the sample mean is greater than 190 grams will be ____?

>95%

between 90% and 95%

between 10% and 20%

<5%

between 80% and 90%

between 5% and 10%

Answer 1

Solution :

Given that ,

mean = = 200

standard deviation = = 33

n = 36

= 200 and

= / n = 33 / 36 = 5.5

P( > 190 ) = 1 - P( < 190)

= 1 - P(( - ) / (190 - 200) / 5.5)

= 1 - P(z < 1.81)   Using standard normal table,

= 1 - 0.9649   

= 0.0351 = 3.51%

P( > 190 ) = < 5%