Question

Same questions different tables.

- X Cumulative standardized normal distribution table, page 1. Given a normal distribution with u 46 ando 5, complete parts (a) through (d) Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view Z0.00 -3.0 0.0014 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 00010 0.0010 2.9 0.0019 0.0018 0.0018 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014 0.08 0.09 0.01 0,02 0.03 0.04 0.05 0.06 0.07 a. What is the probability that X> 37? P(X> 37) (Round to four decimal places as needed.) -2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026 b. What is the probability that X< 36? - 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 (Round to four decimal places as needed.) P(X<36) c. For this distribution. 5% of the values are less than what X-value? - 2.2 00139 00136 00132 00129 00125 00122 0 0119 00116 0 0113 00110 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 X(Round to the nearest integer as needed.) d. Between what two X-values (symmetrically distributed around the mean) are 80% of the values? For this distribution, 80% of the values are between X=and X. -17 0 0446 0 0436 0 0427 o 0418 0.0409 0 0401 0.0392 0.0284 0.027E 67 - 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 00694 0.0681 -1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823 the nearest integer as needed.) (Roundt -1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170 Print Done Enter your answer in each of the answer boxes.

Answer 1

Population mean, µ = 46

Population standard deviation, σ = 5

a) Probability that X >37, P( X > 37) =

= P( (X-µ)/σ > (37 - 46)/5)

= P( z >-1.8)

= 1- P( z <-1.8)

Using Standard normal table:

= 1- 0.0359 = 0.9641

b) Probability that X < 36, P( X < 36) =

= P( (X-µ)/σ < (36 - 46) /5)

= P( z <-2)

Using Standard normal table:

= 0.0228

c) At 5% or 0.05 the value of z closest to this value from the table is, z = -1.645( As the value 0.05 is between -1.64 and -1.65)

Value of X = µ + z*σ = 46+(-1.645)*5 = 37.775 = 38

d) P(-a < Z < a) = 0.80

= P(Z<a) - P(Z< -a) = 0.80

= P(Z<a) - [1 - P(Z< a) = 0.80

= 2P(Z< a) -1 = 0.80

= P(Z<a) = 1.80/2 = 0.90

At or 0.90 the value of z closest to this value from the table is, z = 1.28

Value of lower X = µ + z*σ = 46+(-1.28)*5 = 39

Value of upper X = µ + z*σ = 46+1.28*5 = 52

For this distribution, 80% of the values are between X = 39 and x = 52.

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