(PLZZZ HELP) The lifetime of a certain type of light bulb can be approximated by a normal distribution. The list gives the number of days a bulb can last for 10 light bulbs selected at random. Find the mean and standard deviation of the data set. Then sketch a normal curve to represent the distribution. 24, 24, 32, 13, 22, 34, 20, 26, 17, 28

Arandom sample of n = 25 observations is taken from a n(µ, σ ) population. a 95% confidence interval for µ was calculated to be (42.16, 57.84). the researcher feels that this interval is too wide. you want to reduce the interval to a width at most 12 units. a) for a confidence level of 95%, calculate the smallest sample size needed. b) for a sample size fixed at n = 25, calculate the largest confidence level 100(1 − α)% needed.