The life in hours of a battery is known to be approximately normally distributed, with standard deviation σ = 1.25 hours. a random sample of 10 batteries has a mean life of x overbar equals 40.5 hours.
(a) is there evidence to support the claim that battery life exceeds 40 hours? use α = 0.020.
(b) what is the p-value for the test in part (a)?
(c) what is the β-error for the test in part (a) if the true mean life is 42 hours?
(d) what sample size would be required to ensure that β does not exceed 0.1 if the true mean life is 44 hours?
round your answers to three significant digits.

(a) the battery life ( is or is not ) significantly different greater than 40 hours at α = 0.020.
(b)p-value = round your answer to three decimal places (e. g. 98.765).
(c)β = round your answer to five decimal places (e. g. 98.76543).
(d)