Question

jayla is given the model ( n(361, 18) ) for a set of 75 data values and wants to determine if a normal model would be a good fit for her set. what are the ( -1sigma ) and ( +1sigma ) values for her set? how many data points should she expect to fall within the ( -1sigma ) and ( +1sigma ) values? (2 points) the ( -1sigma ) value is (square). the ( +1sigma ) value is (square). jayla can expect that roughly (square) values should fall between ( -1sigma ) and ( +1sigma ). check answer remaining attempts: 3

Explanation:

Step1: Identify μ and σ

The normal model \(N(\mu, \sigma)\) here has \(\mu = 361\) and \(\sigma = 18\).

Step2: Calculate -1σ value

Subtract σ from μ: \(361 - 18 = 343\).

Step3: Calculate +1σ value

Add σ to μ: \(361 + 18 = 379\).

Step4: Find expected data points

Normal distribution has ~68% data within ±1σ. 68% of 75 is \(0.68 \times 75 = 51\).

Answer:

343; 379; 51