Binomial distribution calculati If n=5 and p=0.5, find P(x=1) Give at least 4 decimal places

Please solve the problem provided in the photo below!!

ages of a variation than ages of females in the general population, so let o = 18.4 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 98% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? The group of 137 randomly selected adult females have a standard deviation of 18.4 years. Assume that the ages of female statistics students have less The required sample size is. (Round up to the nearest whole number as needed.)

Using the inverse transform method for discrete distribution, define a process for generating random variates from a binomial distribution with N=6 and p=0.4. (sixth decimal place.)

Cumulative probability

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded region of the graph. Assume the variable x is normally distributed.                           Standardized Test Composite Scores 28633Score μ=19.7 σ=5.4 28<x<33 x         A graph titled "Standardized Test Composite Scores" has a horizontal x-axis labeled "Score" from about 1 to 39 with tick marks at 6, 28, and 33. A normal curve labeled μ = 19.7 σ = 5.4 is centered above the x-axis at 19.7. Two vertical line segments extend from the curve to the x-axis at 28 and 33. The area below the curve and between the two vertical line segments is shaded and labeled 28 < x < 33.       The probability that the member selected at random is from the shaded area of the graph is enter your response here. ​(Round to four decimal places as​ needed.)

Test a claim that the mean amount of lead in the air in U.S. cities is less than 0.038 microgram per cubic meter. It was found that the mean amount of lead in the air for the random sample of 56 U.S. cities is 0.038 microgram per cubic meter and the standard deviation is 0.068 microgram per cubic meter. At alphaαequals=0.01​, can the claim be​ supported? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.   d) Decide whether to reject or fail to reject the null hypothesis.   ▼   Fail to reject Reject Upper H 0H0 because the standardized test statistic ▼   is is not in the rejection region. ​(e) Interpret the decision in the context of the original claim.   There ▼   is not is enough evidence at the nothing​% level of significance to ▼   reject support the claim that the mean amount of lead in the air in U.S. cities is ▼   equal greater than or equal less than or equal not equal greater than less than nothing…

3 and 4 please