Question

Mona is given the model N (1400,200) for a set of 50 data and wants to make some predictions. About how many data points should she expect to find between 1000 and 1800.

Answer 1

To find out how many data points she should expect to find between 1000 and 1800, she needs to calculate the probability of a data point falling within that range based on the given model N(1400,200).

First, she needs to find the Z-scores for the values 1000 and 1800:

Z-score for 1000:
Z = (1000 - 1400) / 200
Z_1000 = -2

Z-score for 1800:
Z = (1800 - 1400) / 200
Z_1800 = 2

Next, she can use a Z-score table or calculator to find the probabilities associated with these Z-scores:

P(X < 1000) = P(Z < -2) = 0.0228
P(X < 1800) = P(Z < 2) = 0.9772

Now, she can calculate the probability of a data point falling between 1000 and 1800:

P(1000 < X < 1800) = P(X < 1800) - P(X < 1000)
= 0.9772 - 0.0228
= 0.9544

Therefore, she should expect to find approximately 95.44% of the data points falling between 1000 and 1800.

To find the number of data points within that range, she multiplies the total number of data points (50) by the probability:

Expected number of data points = 50 * 0.9544
≈ 47.72

Therefore, Mona should expect to find about 48 data points between 1000 and 1800 based on the given model.