Question

Ah engineer is going to redesign an ejection seat for an airplane. The sest was designed for plots weighing between 120 ib and 171 ib. The new population of plots hat nornaly dstributed weights whth a mean of 126 ib and a standard devation of 34.7 ib Click here to vinw pooe 1 of the ttandard nogmal distribution. Click hece lo virew noge 2 of the standard nomal diatreulion. 2. It a plot is randoenly selected, find the probablity that his weight in between 120 ob and 171k : The pechablity is approvinatoly (Round to four decmal places as needed)

Answer 1

To find the probability that a randomly selected plot's weight is between 120 ib and 171 ib, we need to calculate the z-scores for these weights and use the Z-table to find the corresponding probabilities. The probability is approximately 0.5305.

Step-by-step explanation:

To find the probability that a randomly selected plot's weight is between 120 ib and 171 ib, we need to calculate the z-scores for these weights and use the Z-table to find the corresponding probabilities.

First, let's calculate the z-score for 120 ib:

z = (x - μ) / σ = (120 - 126) / 34.7 ≈ -0.1734

Next, let's calculate the z-score for 171 ib:

z = (x - μ) / σ = (171 - 126) / 34.7 ≈ 1.2964

Using the Z-table, we can find that the probability of a z-score between -0.1734 and 1.2964 is approximately 0.5305.