TABLE 1 Standard Normal Curve Areas Entries in this table pr

TABLE 1 Standard Normal Curve Areas Entries in this table provide cumulative probabilities, that is, the area under the curve to the left of-z. For example, P(Z-_ 1.52) = 0.0643 0.0001 0.0001 0.0001 0.0001 0.0002 0.0003 0.0001 0.0001 0.0001 0.0002 0.0003 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0003 0.0001 0.0001 0.0001 0.0002 0.0003 0.0002 0.0002 0.0003 0.0005 0.0007 0.0003 0.0005 0.0005 0.0008 0.0005 0.0007 0.0010 0.0010 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.0026 0.0035 0.0047 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0025 0.0034 0.0045 0.0023 0.0032 0.0043 0.0023 0.0021 0.0028 0.0038 0.0020 0.0027 0.0041 0.0089 0.0087 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110 0.0179 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0188 0.0183 0.0268 0.0262 0.0244 0.0239 0.0359 0.0436 0.0418 0.0475 0.0582 0.0465 0.0655 0.0630 0.0764 0.0618 0.0778 0.0735 0.0951 0.0901 0.0853 0.0838 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985 0.1230 0.1210 0.1190 0.1170 0.1587 0.1562 0.1539 01515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1814 0.1788 0.1762 0.1736 0.1711 977 578 3050 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121 0.3707 0.3669 0.3632 0.3594 0.3557 0.35 0.3936 0.4602 0.4562 0.4522 0.4483 0.44430.4404 0.43640.4325 0.4286 0.4247 0.4880 SOURE: Probablities calculated with Excel. TABLE 1 (Continued) Entries in this table provide cumulative probabilities, that is, the area under the curve to the left of z. For example, P 1.52) = 0.9357 0.5239 0.5279 0.5319 0.5398 0.5675 0.5714 0.5793 0.6554 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.68440.6879 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7549 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.8264 0.8365 0.8643 0.8849 0.9032 0.9049 0.9066 0.9082 0.8830 0.9015 0.8729 0.8925 0.9207 0.9222 0.9236 0.9251 0.9265 0.9292 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 0.9452 0.9463 0.94740.9484 0.9495 0.9505 0.9515 0.95250.9535 0.9545 0.9554 0.9564 0.9573 0.9582 0.9591 0.9641 0.9599 0.9633 0.9649 0.9656 0.9664 0.9671 0.9678 0.9719 0.9726 0.9732 0.9738 0.97440.9750 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 9842 991 993 993 0.9934 0.9938 997 997 0.9984 0.9988 0.9992 0.9986 0.9987 0.9992 0.9993 0.9993 0.9993 0.9995 0.9995 0.9997 0.9997 0.9997 SOURCE: Probablities cakculated with Excel

Solution

mu =28 and sigma = 2.5

When n = 35 ir n =70 sample size is sufficiently large to assume lthe average to follow a normal distirbution.

Yes

Yes

c) Std error for sample I = std dev/rtn = 2.5/rt35 =0.4226

Std error for sample II = 2.5/rt70 = 0.2988

P(X bar <28.6) for sample I = P(z<0.6/0.4226) = P(Z<1.41)

= 0.0783

For second sample P(Z<0.6/0.2998) = P(Z<2)

= 0.0228