Suppose 25% of home owners in a city have earthquake insurance. Let p be the proportion of

Suppose 25% of home owners in a city have earthquake insurance. Let ˆp be the proportion of earthquake insurance holders from a random sample of 64 homes in this city.

a) Briefly describe why ˆp is a random variable.

(b) Find the mean (expected) value of ˆp

(c) Find the standard deviation of ˆp.

(d) Can we say that the distribution of ˆp is approximately normal? Explain.

(e) Use normal distribution (from the table in the last two pages) to estimate the probability that ˆp ≤ 0.2.

 

 

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The table gives the values of tay where Pr(T, >1v) =a, with v degrees of freedom 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 3.078 6.314 12.076 31.821 63.657 318.310 636.620 31.598 2 1.886 2.920 4.303 6.965 9.925 22.326 1.638 1.533 1.476 2.353 2.132 2.015 3.182 2.776 2.571 4.541 3.747 3.365 10.213 7.173 5.893 12.924 8.610 6.869 5.841 4 5 4.604 4.032 6. 1.440 1.415 1.943 2.447 2.365 3.143 2.998 3.707 3.499 5.208 5.959 5.408 1.896 1.860 1.833 1.812 4.785 4.501 4.297 4.144 8. 9. 10 1.397 1.383 2.306 2.262 2.228 2.896 2.821 2.764 3.355 3.250 3.169 5.041 4.781 1.372 4.587 1.796 1.782 1.771 11 1.363 2.201 2.718 3.106 4.025 4.437 12 13 14 1.356 1.350 1.345 2.179 2.160 2.681 2.650 2.624 3.055 3.012 3.930 3.852 3.787 4.318 4.221 1.761 2.145 2.977 2.947 4.140 4.073 15 1.341 1.753 2.131 2.602 3.733 1.746 1.740 2.583 2.567 2.552 2.539 16 17 1.337 1.333 1.330 1.328 2.120 2.110 3.686 3.646 4.015 3.965 3.922 3.883 2.921 2.898 18 19 3.610 3.579 1.734 2.101 2.093 2.878 2.861 1.729 1.725 20 1.325 2.086 2.528 2.845 3.552 3.850 2.831 2.819 2.807 21 1.323 1.721 2.080 2.074 2.518 3.527 3.819 2.508 2.500 2.492 2.485 3.505 3.485 3.467 3.450 22 23 1.321 1.319 1.717 3.792 1.714 1.318 1.316 2.069 2.064 2.060 2.797 2.787 3.767 3.745 3.725 24 1.711 1.708 25 26 27 1.315 1.706 2.056 2.052 2.048 2.479 2.779 2.771 2.763 3.435 3.707 3.421 3.408 3.396 3.385 1.314 1.703 2.473 3.690 28 29 30 1.313 1.311 1.310 1.701 1.699 1.697 2.045 2.042 2.467 2.462 2.457 2.756 2.750 3.674 3.659 3.646 3.307 3.232 40 60 120 3.551 3.460 3.373 3.291 1.303 1.684 1.671 1.658 1.645 2.021 2.423 1.296 1.289 2.000 1.980 1.960 2.390 2.358 2.326 2.704 2.660 2.617 3.160 3.090 8. 1.282 2.576 The table gives the values of tay where Pr(T, >1v) =a, with v degrees of freedom 0.1 0.05 0.025 0.01 0.005 0.001 0.0005 3.078 6.314 12.076 31.821 63.657 318.310 636.620 31.598 2 1.886 2.920 4.303 6.965 9.925 22.326 1.638 1.533 1.476 2.353 2.132 2.015 3.182 2.776 2.571 4.541 3.747 3.365 10.213 7.173 5.893 12.924 8.610 6.869 5.841 4 5 4.604 4.032 6. 1.440 1.415 1.943 2.447 2.365 3.143 2.998 3.707 3.499 5.208 5.959 5.408 1.896 1.860 1.833 1.812 4.785 4.501 4.297 4.144 8. 9. 10 1.397 1.383 2.306 2.262 2.228 2.896 2.821 2.764 3.355 3.250 3.169 5.041 4.781 1.372 4.587 1.796 1.782 1.771 11 1.363 2.201 2.718 3.106 4.025 4.437 12 13 14 1.356 1.350 1.345 2.179 2.160 2.681 2.650 2.624 3.055 3.012 3.930 3.852 3.787 4.318 4.221 1.761 2.145 2.977 2.947 4.140 4.073 15 1.341 1.753 2.131 2.602 3.733 1.746 1.740 2.583 2.567 2.552 2.539 16 17 1.337 1.333 1.330 1.328 2.120 2.110 3.686 3.646 4.015 3.965 3.922 3.883 2.921 2.898 18 19 3.610 3.579 1.734 2.101 2.093 2.878 2.861 1.729 1.725 20 1.325 2.086 2.528 2.845 3.552 3.850 2.831 2.819 2.807 21 1.323 1.721 2.080 2.074 2.518 3.527 3.819 2.508 2.500 2.492 2.485 3.505 3.485 3.467 3.450 22 23 1.321 1.319 1.717 3.792 1.714 1.318 1.316 2.069 2.064 2.060 2.797 2.787 3.767 3.745 3.725 24 1.711 1.708 25 26 27 1.315 1.706 2.056 2.052 2.048 2.479 2.779 2.771 2.763 3.435 3.707 3.421 3.408 3.396 3.385 1.314 1.703 2.473 3.690 28 29 30 1.313 1.311 1.310 1.701 1.699 1.697 2.045 2.042 2.467 2.462 2.457 2.756 2.750 3.674 3.659 3.646 3.307 3.232 40 60 120 3.551 3.460 3.373 3.291 1.303 1.684 1.671 1.658 1.645 2.021 2.423 1.296 1.289 2.000 1.980 1.960 2.390 2.358 2.326 2.704 2.660 2.617 3.160 3.090 8. 1.282 2.576

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a p is a random variable because p is the proportion of proportion of earthquake insurance holde... View the full answer