The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.35 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months.

Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.

Round your answer to four decimal places.

p=