Assignment 4 Chapter 1 Density Curves and Normal Distributions pp 51 74 Homework 1 3 1 102 1 103 1 104 1 110 1 118 1 119 Density curve area under the curve Population Mean balance point Median M equal area point Always on or above the horizontal axis Total area under the curve 1 Population standard deviation s Normal curve Normal distributions 68 95 5 99 7 Standardization Giving distributions of values equal metrics Z score has a mean of 0 and a standard deviation of 1 Z score for a particular value x Standard normal distribution the distribution of Z scores N 0 1 a distribution with 0 and s 1 Standard normal table Table A pages T2 T3 Identifies the area under the curve to the left of a given value Inverse normal calculations 1 the area associated with a particular value 1 102 p 70 On the chart below draw a normal curve with a mean 30 standard deviation s 8 Now draw a normal curve on the same chart with a mean 30 standard deviation s 12 10 14 18 22 26 30 34 38 42 46 50 54 c How does the normal curve change with a change of s standard deviation Wider or narrower spread 1 103 p 70 On the chart below draw a normal curve with a mean 30 standard deviation s 8 Now draw a normal curve on the same chart with a mean 40 standard deviation s 8 14 18 22 26 30 34 38 42 46 50 54 58 c How does the normal curve change with a change of Moves right or left 1 104 p 70 On the chart below draw a normal distribution with a mean of 150 and a standard deviation of 35 1 Number of words spoken per day women 16 300 s 4800 men 14 100 s 4400 a Women 68 of women speak between 11 500 and 21 100 words per day 95 5 of women speak between 6 700 and 25 900 words per day 99 7 of women speak between 1 900 and 30 700 words per day c Men 68 of men speak between 9 700 and 18 500 words per day 95 5 of men speak between 5 300 and 22 900 words per day 99 7 of men speak between 900 and 27 300 words per day d Do these data support the contention that women speak more than men Probably but statistical software would be required to determine if the number of words differs significantly 1 115 p 72 Figure 1 22 above shows the relative position of the Mean and the Median on a symmetric normal density curve and a skewed normal density curve Use this chart to assist in answering the questions below For each of the three distributions shown above identify which vertical line is the mean and which is the median a upper left distribution mean median b upper right distribution mean median lower distribution mean median 1 118 p 72 Identify the percent or proportion of area under the curve based on criteria indicated Insert the vertical line and shade the portion of the curve requested z 1 75 Proportion under the curve 0401 or 4 01 Table A area associated with z 1 75 9599 Is the value to the right of 1 75 9599 or 1 9599 0401 z 1 75 Proportion under the curve 9599 or 95 99 Table A area associated with z 1 75 9599 The value to the LEFT of 1 75 9599 or 1 9599 0401 z 0 80 Proportion under the curve 7881 or 78 81 Table A area associated with z 80 2119 is the value to the right of 80 2119 or 1 2119 7881 0 80 z 1 75 Proportion under the curve 748 or 74 8 Table A area associated with z 80 2119 Area to the RIGHT of 80 7881 The area associated with z 1 75 9599 Area to the RIGHT of 1 75 0401 Area between the two boundaries 7881 0401 748 1 119 p 72 Identify the percent or proportion of area under the curve based on criteria indicated Insert the vertical line and shade the portion of the curve requested z 1 4 Proportion under the curve 0808 or 8 08 Table A area associates with z 1 40 0808 Is the value to the LEFT of 1 40 0808 or 1 0808 9192 z 1 4 Proportion under the curve 9192 or 91 92 Table A area associates with z 1 40 0808 Is the value to the left of 1 40 0808 or 1 0808 9192 z 2 0 Proportion under the curve 0228 or 2 28 Table A area associates with z 2 00 9772 Is the value to the RIGHT of 2 00 9772 or 1 9772 0228 1 4 z 2 0 Proportion under the curve 8964 or 89 64 Table A area associates with z 1 40 0808 Area to the RIGHT of 1 40 9192 The area associated with z 2 00 9772 Area to the RIGHT of 2 00 0228 Area between the two boundaries 9192 0228 8964 Standardized z scores 2 Given that IQ is described as possessing a mean of 100 and a standard deviation of 15 compute the z scores for the following IQ scores Use the z score formula a IQ 135 z 2 333 b IQ 100 z 0 c IQ 85 z 1 0 d IQ 165 z 4 333 e IQ 42 z 3 87 f IQ 120 z 1 333 3 Below is the density curve of a uniform distribution contrasting with standard normal distribution Just like the standard normal distribution the area under the curve or box in this case equals 1 0 For a uniform distribution all values are equally likely Please identify the mean the median and the quartiles for a uniform distribution 20 30 40 50 60 70 80 90 10 Mean 5 Median 5 Quartiles 25 75