Question

QUESTION PART A: A particular fruit's weights are normally distributed, with a mean of 654 grams and a standard deviation of 30 grams.

If you pick 12 fruit at random, what is the probability that their mean weight will be between 644 grams and 656 grams

QUESTION PART B: A particular fruit's weights are normally distributed, with a mean of 735 grams and a standard deviation of 9 grams.

If you pick 20 fruits at random, then 9% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

Mean = = 654

Standard deviation = = 9

n = 20

= = 654

= / n = 9/ 20 = 8.660254

P(644< <656 )  

= P[(644-654) /8.660254 < ( - ) / < (656-654) /8.660254 )]

= P( -1.1547< Z < 0.23094)

= P(Z <0.23094) - P(Z <-1.1547 )

= 0.124107-0.591319= 0.467213

Probability = 0.467213

……………………………………………………………………………………………..

Mean = = 735

Standard deviation = = 9

n = 20

= = 735

= / n = 9 / 20 = 2.01246

9% greater than

P(Z < z ) = 0.09

1 - P(Z < z ) = 0.09

P(Z <z ) =1 - 0.09 = 0.91

z = 1.340755

= z * + = (1.340755)* 2.01246+ 735

= 737.698

Answer: 738 gram