Question

while testing gas pumps for accuracy across the state, the research team found that out of 6985 pumps, 1299 were inaccurate. use a normal distribution and a known test statistic of z = –2.93. the claim is that less than 20% of the gas pumps across the state are inaccurate. use a 0.01 significance level. find the p-value.

Answer was 0.0017 Please go through the processes of how that is the answer (step by step) so I can understand

Answer 1

Using a normal distribution table look up Z=2.93 and you’ll find it corresponds to a probability of 0.9983, which means that 99.83% of the distribution is within 2.93 standard deviations above the mean. It also means that 100-99.83=0.17% are outside this range. Because of symmetry 0.17% lie in the opposite tail of the distribution, that is, more than 2.93 standard deviations below the mean, represented by Z=-2.93.