Q1.Suppose that a random variable X is normally distributed with mean 91 and standard deviation 8. What is the Z value when X is 132?Please give your answer correctly rounded to two decimal places.

Q2. In a mound shaped symmetric distribution with ? of 100 and ? of 5, within what range would we expect 99% of values to lie?Please give your answers correctly rounded to two decimal places. Your answer for the lower bound:____? Your answer for the upper bound:_____?

Q3. The lifetime of a new smartphone (years) is exponentially distributed with ? = 0.02.

What is the value of the mean lifetime of new smartphone?

Please give your answer correctly rounded to two decimal places.

Please do NOT include units in your answer.

Q4. Suppose that a random variable X is normally distributed with standard deviation 0.6, however the mean is unknown.It is known that 2.5% of values are below an x value of 28.What is the value of the mean?Give your answer correctly rounded to two decimal places.Do NOT include units in your answer

Q5. Let X be an exponential random variable with ? = 0.1.

What is the value of P(X

Please give your answer correctly rounded to two decimal places.

TABLE 4 Critical Values of the Student t Distribution v Degrees of Degrees of Freedom tas Freedom 3.078 6.314 12.706 31 821 43.657 1311 1.699 2.045 2462 2.756 1.886 2.920 4.303 6965 9.925 30 1310 1.697 2.042 2457 2.750 3 1.638 2.353 3.182 4541 5.841 35 1306 1.690 2.030 2438 2.724 1.533 2.132 2.776 3.747 4.604 1303 1.684 2.021 2423 2.704 5 1.476 2.015 2.571 3.365 4.032 45 1301 1679 2.014 2412 2.690 6 1.440 1.943 2.447 3.143 3.707 50 1299 1.676 2.009 2403 2.678 7 1.415 1.895 2.365 2998 3.499 55 1297 1.673 2.004 2396 2.668 8 1.397 1.860 2.306 2.896 3.355 60 1.296 1671 2.000 2390 2.660 9 1.383 1.833 2.262 2.821 3.250 65 1.295 1.669 1.997 2385 2.654 10 1.372 1.812 2.228 2.764 3.169 70 1294 1.667 1.991 2381 2.648 11 1.363 1.796 2.201 2.718 3.106 75 1.293 1.665 1.992 2377 2.643 12 1.356 1.782 2.179 2.681 3.055 80 1 292 1.664 1.990 2374 2.639 13 1.350 1.771 2.160 2.650 3.012 85 1292 1.663 1.986 2371 2.635 14 1.345 1.761 2.145 2.624 2.977 90 1291 1662 1.987 2368 2.632 15 1.341 1.753 2.131 2.602 2947 95 1291 1.661 1.985 2366 2.629 16 1.337 1.746 2.120 2.587 2921 100 1290 1.660 1.984 2364 2.626 17 1.333 1.740 2.110 2567 2.898 110 1289 1659 1.982 2361 2.621 18 1.330 1.734 2.101 2.552 2.878 120 1 289 1.658 1980 2358 2.617 19 1.328 1.729 2093 2.539 2.861 130 1.289 1.657 1.978 2355 2.614 20 1.325 1.725 2.086 2.528 2.845 140 1 288 1.656 1.977 2353 2.611 21 1.323 1.721 2.080 2518 2.831 150 1287 1.655 1.976 2351 2.609 22 1.321 1.717 2074 2508 2.819 160 1287 1.654 1.975 2350 2.607 23 1.319 1.714 2.069 2.500 2.807 170 1287 1.654 1.974 2348 2.605 24 1.318 1,711 2.064 2.492 2.797 180 1285 1.653 1.973 2347 2.603 25 1.316 1.708 2.060 2.485 2.787 190 1286 1.653 1.973 2346 2.602 26 1.315 1.706 2.056 2.479 2.779 200 1286 1653 1.972 2345 2.601 27 1.314 1.703 2.052 2.473 2.771 1.282 1.645 1.960 2326 2.576 28 1.313 1.701 2048 2.467 2.763TABLE 3 Cumulative Standardised Normal Probabilities v P(-00