Please answer any one you know. If you know all, great. If not, I still appreciate it. Please provide a thorough explanation.
1. Assume that the readings on thermometers are normally distributed with a mean of 0 degrees and a standard deviation of 1.00 degree Celsius. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. The given values are in Celsius degrees.
a) Less than -1.00
b) Between -1.80 and 2.08
2. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has an IQ score that is less than 130.
3. Women's heights are normally distributed with a mean of 63.6 in. and a standard deviation of 2.5 in. A social organization for tall people has a requirement that women must be at least 70 in.(or 5 ft 10 in.) tall. What percentage of women meets that requirement?
4. Birth weights in the US are normally distributed with a mean of 3420 g and a standard deviation of 495 g. If a hospital plans to set up special observation conditions for the lightest 2% of babies, what weight is used for the cut-off separating the lightest 2% from the others?
5. Women's heights are normally distributed with a mean of 63.6 in. and a standard deviation of 2.5 in.
a) If 1 woman is randomly selected, find the probability that her height is less than 64 in.
b) If 36 women are randomly selected, find the probability that they have a mean height of less than 64 in.
Note: Apply central limit theorem for part B
6. Assuming that boys and girls are equally likely, estimate the probability of getting more than 36 girls in 64 births. Is it unusual to get more than 36 girls in 64 births?
7. Given the information below regarding a binomial distribution, state whether it is possible or not to use the normal approximation: With n=14, and p=0.4