Answer:
0.8190
Step-by-step explanation:
The weight of Kiwi fruits is normally distributed with an average weight of 76 grams and a standard deviation of 3.6 grams.
We want to find the proportion of Kiwi fruits that have weights between 70 and 80 grams.
We find the z-scores of 70 and 80 using
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
For 70, the z-score is:
[tex]z = \frac{70 - 76}{3.6} = - 1.67[/tex]
The area corresponding to a z-score of -1.67 on the standard normal distribution table is 0.0475
For 80, the z-score is:
[tex]z = \frac{80 - 76}{3.6} = 1.11[/tex]
The area to the corresponding to a z-score of 1.11 is 0.8665
The area between the two z-scores is 0.8665-0.0475=0.8190
Therefore the proportion of Kiwi fruits have weights between 70 and 80 grams is 0.8190
