Random samples of a Gaussian distribution will fall within two standard deviations of the mean with a probability which is approximately 68%. True or False

A population has an average of 125 and a standard deviation of 15.  Calculate the probability that in a sample of size 75, the sample mean is greater than 130.

Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?

Assume time to failure density function (in months) of transplanted kidneys has a Weibull distribution with shape factor of 3 and scale of 6. Use R and answer the following questions (enter your answers with 3 decimal points):

I'm having a hard time on this question. A single toss of a fair coin results in either 0 or 1 head, each with probability 1/2. Define H = number of heads obtained on a single toss. The mean of H is = 0.5 And the standard deviation of H is = 0.5. Suppose you toss a fair coin four times. Define T = total number of heads obtained. Find the mean and standard deviation of T.

The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?

Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 89 and 121.

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal.