Respuesta :
a) Judy's standardized score tells that her bone density is about one and a half standard deviations below the average score for all women her age. The fact that the standardized score is negative(-1.45) indicates that Judy's bone density is below the average for your peer group.
b) 5.52 g/cm²
Given: The standardized score of Judy , Z = -1.45
The mean bone density of 25-year-old women (μ) = 956 g/cm²
Judy's bone density or the Sample bone density (X) = 948 g/cm²
We know the formula:
Z = (X - μ) / σ
where,
Z is the standard value also known as Z-value,
X is the random variable,
μ is the mean value,
σ is the standard deviation
Therefore,
-1.45 = (948 - 956) / σ
σ = -8 / -1.45
σ = 5.5172 ≈ 5.52 g/cm²
Hence, the standard deviation of bone density in the reference population is 5.52 g/cm²
Know more about "standard normal form" here: https://brainly.com/question/13708253
#SPJ4
Disclaimer: The question is incomplete. The complete question is mentioned below:
Measuring bone density Individuals with low bone density have a high risk of broken bones (fractures). Physicians who are concerned about low bone density (osteoporosis) in patients can refer them for specialized testing. Currently, the most common method for testing bone density is dual-energy X-ray absorptiometry (DEXA). A patient who undergoes a DEXA test usually gets bone density results in grams per square centimeter (g/cm²) and in standard units.
Judy, who is 25 years old, has her bone density measured using DEXA. Her results indicate a bone density in the hip of 948 g/cm² and a standardized score of z = -1.45. In reference population of 25-year-old women like Judy, the mean bone density in the hip is 956 g/cm².
(a) Judy has not taken a statistics class in a few years. explain to her in simple language what the standardized score tells her about her bone density.
(b) use the information provided to calculate the standard deviation of bone density in the reference population.
