Suppose that a particular bend in an interstate highway is designed for a maximum speed of 78 mph. Data collected previously show that the top speed for automobiles in dry conditions around this bend is normally distributed with a mean of 67 mph and a standard deviation of 3.3 mph. A researcher for the state's transportation department wants to know if the mean top speed of automobiles going around this bend is still 67 mph or if it has changed. He plans to use a one-sample z ‑test for a population means using the established standard deviation of 3.3 mph. He measures the top speeds of six randomly selected automobiles going around this bend in dry conditions. The speeds of these automobiles, in miles per hour, are given below. 69, 67, 70, 75, 73, 45 Is the researcher justified in using a one-sample z‑test for the mean top speed of all automobiles going around this bend? Why or why not?
a) No, because the sample data has a significant outlier.
b) No, because the population standard deviation is not known.
c) Yes, all the requirements are met. The sample is a simple random sample from a normal population with known standard deviation.
d) No, the population is not known to have a normal distribution.
e) No, because the sample is biased.

Option c) : Yes, all the requirements are met. The sample is a simple random sample from a normal population with known standard deviation.

Step-by-step explanation:

We are given that the data for top speed for automobiles in dry conditions around the particular bend is normally distributed with a mean of 67 mph and a standard deviation of 3.3 mph.

And a one sample z-test is used to check that if the mean top speed of automobiles going around this bend is still 67 mph or if it has changed.

Also, the six randomly selected automobiles are taken from the normal population with standard deviation known.

One sample z-test can be used only when we know population standard deviation and the data is normally distributed.

So, all these conditions suggest that option c) is correct.

side xy = 10

sin(x) = 4/5

cos(x) = 3/5

tan(x) = 4/3

step-by-step explanation:

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.