Question

The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a

mean diameter of 22 mm and a standard deviation of 2.5 mm. What proportion of such tomatoes have a diameter
greater than 25 mm?
Find the z-table here.
O 0.1151
O 0.1539
0.8461
0.8849

Answer 1

Hi, that would be option 3 if I am correct.

Hope this helps.

Answer 2

0.8461

To find the proportion of cherry tomatoes that have a diameter greater than 25 mm, we need to determine the proportion of the distribution that falls above this value. We can do this by converting the diameter of 25 mm to a z-score using the formula:

z-score = (value - mean) / standard deviation

For a diameter of 25 mm, the z-score is (3 - 22) / 2.5 = -2.8.

We can then use a z-table to find the proportion of the distribution that falls above this value. The z-table gives the area under the standard Normal curve to the left of a given z-score. To find the proportion of the distribution above the diameter of 25 mm, we need to find the area to the right of -2.8. From the z-table, we find that the area to the right of -2.8 is 0.8461. Therefore, approximately 84.61% of cherry tomatoes produced by the farm have a diameter greater than 25 mm.