Question

If the mean height of bonsai trees is 52 cm with a standard deviation of 10 cm, 95% of the trees are between

Answer 1

In a normal distribution of bonsai tree heights with a mean of 52 cm and a standard deviation of 10 cm, approximately 95% of trees fall between 32 cm and 72 cm in height.

To find the range within which 95% of the bonsai trees' heights lie, we'll use the properties of a normal distribution.

Given:

Mean height
`(\(\mu\))` = 52 cm

Standard deviation
`(\(\sigma\))` = 10 cm

We'll use the formula for a normal distribution to determine the range within which 95% of the data falls, which is within approximately 2 standard deviations from the mean.

Calculate the interval:

Lower Limit:
`\( \mu - 2\sigma \)`

`\[ \text{Lower Limit} = 52 - 2 * 10 = 52 - 20 = 32 \text{ cm} \]`

Upper Limit:
`\( \mu + 2\sigma \)`

`\[ \text{Upper Limit} = 52 + 2 * 10 = 52 + 20 = 72 \text{ cm} \]`

Therefore, using this calculation, we've determined that 95% of the bonsai trees' heights fall within the range of 32 cm to 72 cm.

complete the question

If the mean height of bonsai trees is 52 cm with a standard deviation of 10 cm, 95% of the trees are between □ cm and □ cm.