Question

the mean height of a group of plants is 20 centimeters, with a standard deviation of 3 centimeters. what is the probability that a randomly selected plant is between 20.2 cm and 24.9 cm tall? (1 point) 40.02 44.25 43.85 42.85

Explanation:

Step1: Calculate z - scores

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 20\) (mean), \(\sigma=3\) (standard deviation).
For \(x = 20.2\), \(z_1=\frac{20.2 - 20}{3}=\frac{0.2}{3}\approx0.07\).
For \(x = 24.9\), \(z_2=\frac{24.9 - 20}{3}=\frac{4.9}{3}\approx1.63\).

Step2: Look up z - scores in the table

From the standard normal distribution table:
When \(z = 0.07\), the cumulative probability \(P(Z\leq0.07)\) is \(0.5279\).
When \(z = 1.63\), the cumulative probability \(P(Z\leq1.63)\) is \(0.9484\).

Step3: Calculate the probability between the two z - scores

The probability \(P(0.07<Z<1.63)=P(Z < 1.63)-P(Z < 0.07)\).
\(P(0.07<Z<1.63)=0.9484 - 0.5279=0.4205\)

Answer:

\(42.05\) (assuming the options are percentages, and this value is closest to one of the likely intended options based on the calculation)