Use the cumulative standardized normal distribution table for given questions
| Z |
0.00 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
| -3.0 |
0.0014 |
0.0013 |
0.0013 |
0.0012 |
0.0012 |
0.0011 |
0.0011 |
0.0011 |
0.0010 |
0.0010 |
| -2.9 |
0.0019 |
0.0018 |
0.0018 |
0.0017 |
0.0016 |
0.0016 |
0.0015 |
0.0015 |
0.0014 |
0.0014 |
| -2.8 |
0.0026 |
0.0025 |
0.0024 |
0.0023 |
0.0023 |
0.0022 |
0.0021 |
0.0021 |
0.0020 |
0.0019 |
| -2.7 |
0.0035 |
0.0034 |
0.0033 |
0.0032 |
0.0031 |
0.0030 |
0.0029 |
0.0028 |
0.0027 |
0.0026 |
| -2.6 |
0.0047 |
0.0045 |
0.0044 |
0.0043 |
0.0041 |
0.0040 |
0.0039 |
0.0038 |
0.0037 |
0.0036 |
| -2.5 |
0.0062 |
0.0060 |
0.0059 |
0.0057 |
0.0055 |
0.0054 |
0.0052 |
0.0051 |
0.0049 |
0.0048 |
| -2.4 |
0.0082 |
0.0080 |
0.0078 |
0.0075 |
0.0073 |
0.0071 |
0.0069 |
0.0068 |
0.0066 |
0.0064 |
| -2.3 |
0.0107 |
0.0104 |
0.0102 |
0.0099 |
0.0096 |
0.0094 |
0.0091 |
0.0089 |
0.0087 |
0.0084 |
| -2.2 |
0.0139 |
0.0136 |
0.0132 |
0.0129 |
0.0125 |
0.0122 |
0.0119 |
0.0116 |
0.0113 |
0.0110 |
| -2.1 |
0.0179 |
0.0174 |
0.0170 |
0.0166 |
0.0162 |
0.0158 |
0.0154 |
0.0150 |
0.0146 |
0.0143 |
| -2.0 |
0.0228 |
0.0222 |
0.0217 |
0.0212 |
0.0207 |
0.0202 |
0.0197 |
0.0192 |
0.0188 |
0.0183 |
| -1.9 |
0.0287 |
0.0281 |
0.0274 |
0.0268 |
0.0262 |
0.0256 |
0.0250 |
0.0244 |
0.0239 |
0.0233 |
| -1.8 |
0.0359 |
0.0351 |
0.0344 |
0.0336 |
0.0329 |
0.0322 |
0.0314 |
0.0307 |
0.0301 |
0.0294 |
| -1.7 |
0.0446 |
0.0436 |
0.0427 |
0.0418 |
0.0409 |
0.0401 |
0.0392 |
0.0384 |
0.0375 |
0.0367 |
| -1.6 |
0.0548 |
0.0537 |
0.0526 |
0.0516 |
0.0505 |
0.0495 |
0.0485 |
0.0475 |
0.0465 |
0.0455 |
| -1.5 |
0.0668 |
0.0655 |
0.0643 |
0.0630 |
0.0618 |
0.0606 |
0.0594 |
0.0582 |
0.0571 |
0.0559 |
| -1.4 |
0.0808 |
0.0793 |
0.0778 |
0.0764 |
0.0749 |
0.0735 |
0.0721 |
0.0708 |
0.0694 |
0.0681 |
| -1.3 |
0.0968 |
0.0951 |
0.0934 |
0.0918 |
0.0901 |
0.0885 |
0.0869 |
0.0853 |
0.0838 |
0.0823 |
| -1.2 |
0.1151 |
0.1131 |
0.1112 |
0.1093 |
0.1075 |
0.1056 |
0.1038 |
0.1020 |
0.1003 |
0.0985 |
| -1.1 |
0.1357 |
0.1335 |
0.1314 |
0.1292 |
0.1271 |
0.1251 |
0.1230 |
0.1210 |
0.1190 |
0.1170 |
| -1.0 |
0.1587 |
0.1562 |
0.1539 |
0.1515 |
0.1492 |
0.1469 |
0.1446 |
0.1423 |
0.1401 |
0.1379 |
| -0.9 |
0.1841 |
0.1814 |
0.1788 |
0.1762 |
0.1736 |
0.1711 |
0.1685 |
0.1660 |
0.1635 |
0.1611 |
| -0.8 |
0.2119 |
0.2090 |
0.2061 |
0.2033 |
0.2005 |
0.1977 |
0.1949 |
0.1922 |
0.1894 |
0.1867 |
| -0.7 |
0.2420 |
0.2388 |
0.2358 |
0.2327 |
0.2296 |
0.2266 |
0.2236 |
0.2206 |
0.2177 |
0.2148 |
| -0.6 |
0.2743 |
0.2709 |
0.2676 |
0.2643 |
0.2611 |
0.2578 |
0.2546 |
0.2514 |
0.2482 |
0.2451 |
| -0.5 |
0.3085 |
0.3050 |
0.3015 |
0.2981 |
0.2946 |
0.2912 |
0.2877 |
0.2843 |
0.2810 |
0.2776 |
| -0.4 |
0.3446 |
0.3409 |
0.3372 |
0.3336 |
0.3300 |
0.3264 |
0.3228 |
0.3192 |
0.3156 |
0.3121 |
| -0.3 |
0.3821 |
0.3783 |
0.3745 |
0.3707 |
0.3669 |
0.3632 |
0.3594 |
0.3557 |
0.3520 |
0.3483 |
| -0.2 |
0.4207 |
0.4168 |
0.4129 |
0.4090 |
0.4052 |
0.4013 |
0.3974 |
0.3936 |
0.3897 |
0.3859 |
| -0.1 |
0.4602 |
0.4562 |
0.4522 |
0.4483 |
0.4443 |
0.4404 |
0.4364 |
0.4325 |
0.4286 |
0.4247 |
| -0.0 |
0.5000 |
0.4960 |
0.4920 |
0.4880 |
0.4840 |
0.4801 |
0.4761 |
0.4721 |
0.4681 |
0.4641 |
| Z |
0.00 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
| 0.0 |
0.5000 |
0.5040 |
0.5080 |
0.5120 |
0.5160 |
0.5199 |
0.5239 |
0.5279 |
0.5319 |
0.5359 |
| 0.1 |
0.5398 |
0.5438 |
0.5478 |
0.5517 |
0.5557 |
0.5596 |
0.5636 |
0.5675 |
0.5714 |
0.5753 |
| 0.2 |
0.5793 |
0.5832 |
0.5871 |
0.5910 |
0.5948 |
0.5987 |
0.6026 |
0.6064 |
0.6103 |
0.6141 |
| 0.3 |
0.6179 |
0.6217 |
0.6255 |
0.6293 |
0.6331 |
0.6368 |
0.6406 |
0.6443 |
0.6480 |
0.6517 |
| 0.4 |
0.6554 |
0.6591 |
0.6628 |
0.6664 |
0.6700 |
0.6736 |
0.6772 |
0.6808 |
0.6844 |
0.6879 |
| 0.5 |
0.6915 |
0.6950 |
0.6985 |
0.7019 |
0.7054 |
0.7088 |
0.7123 |
0.7157 |
0.7190 |
0.7224 |
| 0.6 |
0.7257 |
0.7291 |
0.7324 |
0.7357 |
0.7389 |
0.7422 |
0.7454 |
0.7486 |
0.7518 |
0.7549 |
| 0.7 |
0.7580 |
0.7612 |
0.7642 |
0.7673 |
0.7704 |
0.7734 |
0.7764 |
0.7794 |
0.7823 |
0.7852 |
| 0.8 |
0.7881 |
0.7910 |
0.7939 |
0.7967 |
0.7995 |
0.8023 |
0.8051 |
0.8078 |
0.8106 |
0.8133 |
| 0.9 |
0.8159 |
0.8186 |
0.8212 |
0.8238 |
0.8264 |
0.8289 |
0.8315 |
0.8340 |
0.8365 |
0.8389 |
| 1.0 |
0.8413 |
0.8438 |
0.8461 |
0.8485 |
0.8508 |
0.8531 |
0.8554 |
0.8577 |
0.8599 |
0.8621 |
| 1.1 |
0.8643 |
0.8665 |
0.8686 |
0.8708 |
0.8729 |
0.8749 |
0.8770 |
0.8790 |
0.8810 |
0.8830 |
| 1.2 |
0.8849 |
0.8869 |
0.8888 |
0.8907 |
0.8925 |
0.8944 |
0.8962 |
0.8980 |
0.8997 |
0.9015 |
| 1.3 |
0.9032 |
0.9049 |
0.9066 |
0.9082 |
0.9099 |
0.9115 |
0.9131 |
0.9147 |
0.9162 |
0.9177 |
| 1.4 |
0.9192 |
0.9207 |
0.9222 |
0.9236 |
0.9251 |
0.9265 |
0.9279 |
0.9292 |
0.9306 |
0.9319 |
| 1.5 |
0.9332 |
0.9345 |
0.9357 |
0.9370 |
0.9382 |
0.9394 |
0.9406 |
0.9418 |
0.9429 |
0.9441 |
| 1.6 |
0.9452 |
0.9463 |
0.9474 |
0.9484 |
0.9495 |
0.9505 |
0.9515 |
0.9525 |
0.9535 |
0.9545 |
| 1.7 |
0.9554 |
0.9564 |
0.9573 |
0.9582 |
0.9591 |
0.9599 |
0.9608 |
0.9616 |
0.9625 |
0.9633 |
| 1.8 |
0.9641 |
0.9649 |
0.9656 |
0.9664 |
0.9671 |
0.9678 |
0.9686 |
0.9693 |
0.9699 |
0.9706 |
| 1.9 |
0.9713 |
0.9719 |
0.9726 |
0.9732 |
0.9738 |
0.9744 |
0.9750 |
0.9756 |
0.9761 |
0.9767 |
| 2.0 |
0.9772 |
0.9778 |
0.9783 |
0.9788 |
0.9793 |
0.9798 |
0.9803 |
0.9808 |
0.9812 |
0.9817 |
| 2.1 |
0.9821 |
0.9826 |
0.9830 |
0.9834 |
0.9838 |
0.9842 |
0.9846 |
0.9850 |
0.9854 |
0.9857 |
| 2.2 |
0.9861 |
0.9864 |
0.9868 |
0.9871 |
0.9875 |
0.9878 |
0.9881 |
0.9884 |
0.9887 |
0.9890 |
| 2.3 |
0.9893 |
0.9896 |
0.9898 |
0.9901 |
0.9904 |
0.9906 |
0.9909 |
0.9911 |
0.9913 |
0.9916 |
| 2.4 |
0.9918 |
0.9920 |
0.9922 |
0.9925 |
0.9927 |
0.9929 |
0.9931 |
0.9932 |
0.9934 |
0.9936 |
| 2.5 |
0.9938 |
0.9940 |
0.9941 |
0.9943 |
0.9945 |
0.9946 |
0.9948 |
0.9949 |
0.9951 |
0.9952 |
| 2.6 |
0.9953 |
0.9955 |
0.9956 |
0.9957 |
0.9959 |
0.9960 |
0.9961 |
0.9962 |
0.9963 |
0.9964 |
| 2.7 |
0.9965 |
0.9966 |
0.9967 |
0.9968 |
0.9969 |
0.9970 |
0.9971 |
0.9972 |
0.9973 |
0.9974 |
| 2.8 |
0.9974 |
0.9975 |
0.9976 |
0.9977 |
0.9977 |
0.9978 |
0.9979 |
0.9979 |
0.9980 |
0.9981 |
| 2.9 |
0.9981 |
0.9982 |
0.9982 |
0.9983 |
0.9984 |
0.9984 |
0.9985 |
0.9985 |
0.9986 |
0.9986 |
| 3.0 |
0.9987 |
0.9987 |
0.9987 |
0.9988 |
0.9988 |
0.9989 |
0.9989 |
0.9989 |
0.9990 |
0.9990 |
1. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d)
a. What is the probability that Z is less than 1.54?
b. What is the probability that Z is greater than 1.82?
c. What is the probability that Z is between 1.54 and 1.82?
d. What is the probability that Z is less than 1.541.54 or greater than 1.82?
2. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d) below.
a. What is the probability that Z is between -1.55 and 1.83?
b. What is the probability that Z is less than -1.58 or greater than 1.85?
c. What is the value of Z if only 3% of all possible Z values are larger?
d. Between what two values of Z (symmetrically distributed around the mean) will 97.86% of all possible Z values be contained?
3. Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), determine the following probabilities.
a. P(Z>1.02) b. P(Z<-0.22) c. P(-1.96 d. What is the value of Z if only 30.85% of all possible Z-values are larger?
4. Given a normal distribution with μ=48 and σ=4, complete parts (a) through (d).
a. What is the probability that X > 43?
b. What is the probability that X < 45?
c. For this distribution, 10% of the values are less than what X-value?
d. Between what two X-values (symmetrically distributed around the mean) are 80% of the values?
5. The annual per capita consumption of bottled water was 34.3 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 34.3 and a standard deviation of 12 gallons.
a. What is the probability that someone consumed more than 39 gallons of bottled water?
b. What is the probability that someone consumed between 30 and 40 gallons of bottled water?
c. What is the probability that someone consumed less than 30 gallons of bottled water?
d. 99.5% of people consumed less than how many gallons of bottled water?
6. One year consumers spent an average of $23 on a meal at a resturant. Assume that the amount spent on a resturant meal is normally distributed and that the standard deviation is $4. Complete parts? (a) through (c) below.
a. What is the probability that a randomly selected person spent more than $26?
b. What is the probability that a randomly selected person spent between $14 and $22?
c. Between what two values will the middle 95% of the amounts of cash spent fall?
7. A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 78 and a standard deviation of 7. Complete parts (a) through (d).
a. What is the probability that a student scored below 85 on this exam?
b. What is the probability that a student scored between 65 and 97?
c. The probability is 15% that a student taking the test scores higher than what grade?
d. If the professor grades on a curve (for example, the professor could give? A's to the top 10% of the class, regardless of the score), is a student better off with a grade of 92 on this exam or a grade of 67 on a different exam, where the mean is 63 and the standard deviation is 4? Show your answer statistically and explain.