Question

1. Blood Pressures. Among human females, systolic blood pressure (measured in mmHg) is normally distributed, with a mean of and a standard deviation of 06.3, μ = 1 .9. σ = 8 a. Connie’s blood pressure is 117.4 mmHg. Calculate the z-score for her blood pressure.

b. Mark Connie’s x-value and z-score (as well as the mean) in the correct locations on the graph. c. Interpret the meaning of Connie’s z-score value. 2. Finding raw values from z-scores. California condors are among the largest birds in North America, with wingspans of around 10 feet. Among the California condor population, let’s suppose that wingspans are normally distributed, with a mean of 106 inches, and a standard deviation of 5 inches. The California condor pictured has a wingspan corresponding to a z-score of -0.6. Determine the condor’s actual wingspan in inches; show your work. Place the z-score and x-value for the condor’s wingspan on the graph, along with the mean.

3. Using z-Scores to Compare Data from Different Distributions. Before applying to law school in the US students need to take the LSAT. Before applying to medical school, students need to take the MCAT. Here are some summaries for each (both are normally distributed): the Mean Standard deviation LSAT 51 μ = 1 0 σ = 1 MCAT 5.1 μ = 2 .4 σ = 6 Juwan took both. He scored 172 on the LSAT and 37 on the MCAT. On which the did he do relatively better compared to other test takers? Justify your answer below; show your work and explain your reasoning. LSAT Scores MCAT Scores

Answer 1

By definition of Z score, for a random variable X, with Mean and Standard Deviation :

a. Given:

For X = 117.4,

b. Graphing the X value, Mean and Z score:

Connie’s z-score value implies that Connie's score is 14.44 standard deviations above the mean score.

2.

The California condor pictured has a wingspan corresponding to a z-score of -0.6

3.

LSAT 5.1:

MCAT 5.1

From standard normal table, any value Z > 4 would represent a 100% percentile. Here, LSAT 5.1 Z score is far greater than the MSAT 5.1 Z score. Hence, Juwan is found to have scored relatively better in LSAT than MSAT.