A medical researcher collected the systolic blood pressure reading for a random sample of n = 30 female students under the age of 21 who visited the Student's Health Service. The blood pressures are:

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120 122 121 108 133 119 136 108 106 105 122 139 133 115 104 94 118 93 102 114 123 125 124 108 111 134 107 112 109 125 Assume that systolic blood pressure comes from a normal (,) distri- bution where the standard deviation = 12 is known. (a) Use a normal (120, 152) prior for . Calculate the posterior distribu- tion of p. (b) Find a 95% Bayesian credible interval for u. (c) Suppose we had not actually known the standard deviation . In- stead, the value = 12 was calculated from the sample and used == in place of the unknown true value. Recalculate the 95% Bayesian credible interval.