Chapter 5 Extra Practice
5.1 Point Estimation and Sampling Distributions
1. The specific absorption rate (SAR) for a cell phone measures the amount of radio frequency (RF) energy absorbed by the user’s body when using the handset. Every cell phone emits RF energy. Different phone models have different SAR measures. To receive certification from the Federal Communications Commission (FCC) for sale in the United States, the SAR level for a cell phone must be no more than 1.6 watts per kilogram. The figure below shows the highest SAR level for a random selection of cell phone models as measured by the FCC.[1] Find a point estimate of the true (population) mean of the specific absorption rates (SARs) for cell phones.
| Phone model | SAR | Phone model | SAR | Phone model | SAR |
|---|---|---|---|---|---|
| Apple iPhone 4S | 1.11 | LG Ally | 1.36 | Pantech Laser | 0.74 |
| BlackBerry Pearl 8120 | 1.48 | LG AX275 | 1.34 | Samsung Character | 0.5 |
| BlackBerry Tour 9630 | 1.43 | LG Cosmos | 1.18 | Samsung Epic 4G Touch | 0.4 |
| Cricket TXTM8 | 1.3 | LG CU515 | 1.3 | Samsung M240 | 0.867 |
| HP/Palm Centro | 1.09 | LG Trax CU575 | 1.26 | Samsung Messager III SCH-R750 | 0.68 |
| HTC One V | 0.455 | Motorola Q9h | 1.29 | Samsung Nexus S | 0.51 |
| HTC Touch Pro 2 | 1.41 | Motorola Razr2 V8 | 0.36 | Samsung SGH-A227 | 1.13 |
| Huawei M835 Ideos | 0.82 | Motorola Razr2 V9 | 0.52 | SGH-a107 GoPhone | 0.3 |
| Kyocera DuraPlus | 0.78 | Motorola V195s | 1.6 | Sony W350a | 1.48 |
| Kyocera K127 Marbl | 1.25 | Nokia 1680 | 1.39 | T-Mobile Concord | 1.38 |
Figure 5.15
2. A student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms. She surveys 600 students and finds that 480 are against the new legislation. Find a point estimate of the true (population) proportion of students in the school district who are against the new legislation.
5.2 The Sampling Distribution of the Sample Mean (CLT)
1. The length of time, in hours, it takes an “over 40” group of people to play one soccer match is normally distributed with a mean of two hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population. Find the probability that the sample mean is between 1.8 hours and 2.3 hours.
- Let X = the time, in hours, it takes to play one soccer match.
- The probability question asks you to find a probability for the sample mean time, in hours, it takes to play one soccer match.
- Let = the mean time, in hours, it takes to play one soccer match.
- If μX = , σX = , and n = , then X ~ N( , ) by the central limit theorem for means.
- Find P(1.8 < < 2.3). Draw a graph.
2. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours.[2] A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours.
3. In a recent s