An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 161 lb. The new population of pilots has normally distributed weights with a mean of 127 lb and a standard deviation of 25.9 lb. Click here to view page 1 of the standard normal distribution. Click here to view page 2 of the standard normal distribution. a. If a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb. The probability is approximately . (Round to four decimal places as needed.) b. If 30 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 161 lb. The probability is approximately . (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? O A. Part (a) because the seat performance for a single pilot is more important. O B. Part (b) because the seat performance for a sample of pilots is more important. O C. Part (a) because the seat performance for a sample of pilots is more important. O D. Part (b) because the seat performance for a single pilot is more important.Standard normal distribution table (page 1) Standard Normal (z) Distribution: Cumulative Area from the LEFT Z 00 .01 .02 .03 .04 .05 .06 .07 .08 .09 -3.50 and lower .0001 -3.4 .0003 0003 .0003 .0003 0003 .0003 .0003 .0003 0003 .0002 -3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003 -3.2 .0007 0007 .0006 .0006 .0006 .0006 0006 .0005 .0005 .0005 - 3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007 -3.0 .0013 0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010 -2.9 .0019 0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 0020 .0019 -2.7 .0035 0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026 -2.6 .0047 0045 .0044 .0043 .0041 .0040 .0039 .0038 0037 .0036 -2.5 .0062 0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064 -2.3 .0107 0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084 -2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143 -2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183 - 1.9 .0287 .0281 .0274 .0268 .0262 .0256 .0250 .0244 .0239 .0233 - 1.8 .0359 .0351 .0344 .0336 0329 .0322 .0314 .0307 0301 .0294