Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Examples for Ch 7

### Elementary Statistics

Question | Answer |
---|---|

If the scores for a test have a mean of 100 and a standard deviation of 15, find the percentage of scores that will fall below 112. | X= 112, μ= 100, σ= 15; z=(X-μ)/σ =(112-100)/15 = 12/15 = 0.8; area = .7881, 78.81% of the scores will fall below 112. |

Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. Find the propility of its generating between 27 and 31 pounds per month. | X₁= 27, X₂=31, μ= 28, σ= 2; z₁=(X₁-μ)/σ =(27-28)/2 = 3/2 = -0.5; z₂=(X₂-μ)/σ =(31-28)/2 = 1.5; area = .6247; There a 62.47% propability that a household will generate between 27 and 31 pounds of newspapers. |

The average time it takes to respond to an emergency call is 25 minutes with a standard deviation of 4.5 minutes. If 80 calls are randomly selected, approximately how many will be respond to in less than 15 minutes? | X= 15, μ= 25, σ= 4.5; z=(X-μ)/σ =(15-25)/4.5 = -2.22; area = .0132; n*area = 80(.0132)=1.056; Therefore, approximately one call will be responded to in under 15 minutes. |

In order to qualify for a police academy, candidates must scorein the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. | 10%= .1= .1000= area; 1-area= 1-.1000= .9000; z=1.28; X= ?, μ= 200, σ= 20; z=(X-μ)/σ; 1.28= (X-200)/20; X = 226; A score of 226 is the cutoff. |

The average age of a vehicle registered in the United States is 8 years, or 96 months. Standard deviation is 16 months. If a sample of 36 vehicles is selected, find the propability that the mean of their age is between 90 and 100 months. | ¯X₁=90, ¯X₂=100, μ= 96, σ= 16, n=36; z=(¯X- μ)/(σ/√n); z₁=(90-96)/(16/√36)=-2.25; z₂=(100-96)/(16/√36)=1.50; area = 0.921; The propability of obtaining a sample mean between 90 and 100 months is 92.1%. |

If a baseball player's batting average is 0.320 (32%), find the propability that the player will get at most 26 hits in 100 times at bat. | X= 26, p=0.32, q=1-p=1-.32=.68, n=100; μ=np=(100)(.32)=32; σ=√npq= √(100)(.32)(.68)=4.66; P(X≤26), P(X<26+.5)=P(X<26.5); z=(X-μ)/σ = (26.5-32)/4.66=-1.18; area = .1190 or 11.9%. |

q= | Make sure p is in decimals: 1-p = q |

Find the area under the normal distribution curve between z= 0 and z=2.34. | Area = .4904 |

Find the area right of z=1.11. | Area for z=1.11 is .8665; 1-.8665= .1335 or 11.35%. |

Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds. Find the propility of its generating more than 30.2 pounds per month. | X= 30.2, μ= 28, σ= 2; z=(X-μ)/σ =(30.2-28)/2 = 2.2/2 = 1.1; area = .1357; There a 13.57% propability that a household will generate more than 30.2 pounds of newspapers. |

Created by:
dengler