Let X denote the mean of a random sample of size 25 from a gamma-type distribution with α = 4 and β > 0. Use the Central Limit Theorem to find an approximate 0.9544 confidence interval for β, the mean of the gamma distribution. Hint: Use the random variable (X − 4β)/ p 4β 2/25 = 5X/2β − 10.

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

If a • b*2 = 1.8 x 10*-7, and c•b/d = 7.2 x 10*-4, find the value of a•d*2/c*2

Find all the values of x that make 0.1x + 0.25(102 - x) < 17.10 true.