The Blood Platelet Counts Of A Group Of Women Have A ✓ Solved
The Blood Platelet Counts Of A Group Of Women Have A
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 250.8 and a standard deviation of 65.5. Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 185.3 and 316.3?
b. What is the approximate percentage of women with platelet counts between 54.3 and 447.3?
Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 72.7 Mbps. Using the following instructions, answer the questions:
a. What is the difference between the carrier's highest data speed and the mean of all 50 data speeds?
b. How many standard deviations is that [the difference found in part (a)]?
c. Convert the carrier's highest data speed to a z score.
d. If we consider data speeds that convert to z scores between −2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?
Use z scores to compare the given values. Based on sample data, newborn males have weights with a mean of 3227.7g and a standard deviation of 581.8 g. Newborn females have weights with a mean of 3007.4 g and a standard deviation of 578.4 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
Find the percentile corresponding to the data speed 11.1 Mbps.
Find Q1.
Find P60.
Use the given data to construct a boxplot and identify the 5-number summary from the ratings of males by females in a speed dating experiment.
Use the given data to construct a boxplot and identify the 5-number summary from measured radiation absorption rates (in W/kg) corresponding to 11 cell phones.
Paper For Above Instructions
The blood platelet counts of a group of women show a bell-shaped distribution, which fits well within the normal distribution framework. The provided mean is 250.8 (in thousands of cells/μL), and the standard deviation is 65.5 (again in thousands of cells/μL). Based on the empirical rule, we can determine the percentage of women whose platelet counts fall within specified intervals.
Part A: Percentage of Women with Platelet Counts within 1 Standard Deviation
According to the empirical rule, approximately 68% of the data in a normal distribution lies within one standard deviation from the mean. Therefore, women with platelet counts between 185.3 (250.8 - 65.5) and 316.3 (250.8 + 65.5) are expected to account for around 68% of the sample population. This reflects the bulk of the data clustering around the mean.
Part B: Percentage of Women with Platelet Counts Between 54.3 and 447.3
The range from 54.3 to 447.3 encompasses counts well beyond two standard deviations from the mean, which suggests that this interval covers nearly all women in the study. The empirical rule indicates that approximately 95% of the data falls within two standard deviations from the mean. Therefore, more than 95% of women have platelet counts between 54.3 and 447.3.
Data Speeds of a Smartphone Carrier
The highest measured data speed for a smartphone carrier at 50 airports is 72.7 Mbps, while the mean speed is 16.65 Mbps with a standard deviation of 34.84 Mbps.
Part A: Difference Between Carrier's Highest Data Speed and Mean
The difference between the highest data speed (72.7 Mbps) and the mean (16.65 Mbps) is calculated as follows:
Difference = 72.7 Mbps - 16.65 Mbps = 56.05 Mbps
Part B: Standard Deviations of the Difference
To find how many standard deviations this difference represents, we divide the difference by the standard deviation:
Number of Standard Deviations = Difference / Standard Deviation = 56.05 / 34.84 ≈ 1.61
Part C: Z Score of Carrier's Highest Data Speed
The z score is computed using the following formula:
Z = (X - μ) / σ = (72.7 - 16.65) / 34.84 ≈ 1.61
Part D: Significance of Data Speed
Since the z score of 1.61 is within the range of -2 to 2, the carrier's highest data speed is considered neither significantly low nor significantly high, indicating it is not statistically significant.
Comparison of Newborn Weights
For newborn males, the mean weight is 3227.7 g, with a standard deviation of 581.8 g; for females, the mean is 3007.4 g with a standard deviation of 578.4 g. To determine who is more extreme, we calculate the z scores for both a male and a female weighing 1700 g.
Z Score Calculation for Male
Z_male = (1700 - 3227.7) / 581.8 ≈ -2.66
Z Score Calculation for Female
Z_female = (1700 - 3007.4) / 578.4 ≈ -2.25
Thus, the male newborn weighing 1700 g has a more extreme z score (-2.66) compared to the female (-2.25).
Finding Percentiles and Quartiles
For data speeds of 11.1 Mbps, the analysis of the percentiles can yield relevant insights regarding data distribution and comparison across measures. The computation of Q1 and P60 can provide significant information about the range and concentration of the data.
Boxplot Analysis for Speed Dating Ratings
The ratings of males by females can be accumulated to establish a boxplot that reveals the five-number summary: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
Boxplot Analysis for Radiation Absorption Rates
For assessed radiation absorption rates, we can create boxplots to identify data outliers and summarize the dataset effectively using the five-number summary.
References
- "Applied Statistics for Engineers and Scientists" by David C. Montgomery and George C. Runger.
- "Statistics" by David S. Moore, William I. Notz, and Michael A. example.
- "Practical Statistics for Data Scientists" by Peter Bruce and Andrew Bruce.
- "Statistics for Business and Economics" by Paul Newbold, William L. Carver, and Betty Thorne.
- "The Elements of Statistical Learning" by Trevor Hastie, Robert Tibshirani, and Jerome Friedman.
- "Statistical Inference" by George Casella and Roger L. Berger.
- "Data Analysis Using Regression and Multilevel/Hierarchical Models" by David A. S. Bartholomew.
- "Statistics: An Introduction" by Richard U. Chase.
- "Introduction to the Practice of Statistics" by David S. Moore, George P. McCabe, and Bruce A. Craig.