normal distribution associated probability

Solve the following:
1. Assume that the thermometer readings are normally distributed with a mean of 0° C and a standard deviation of 1.00° C. A thermometer is randomly selected and tested. For each case given below, draw a sketch and find the probability. The given values are in Celsius degrees.
[Note: If using a calculator or MS Excel instead of Table A-2, round answers to four decimal places.]
a. Less than -2.75
b. Greater than 2.33
c. Between 1.00 and 3.00

2. Find the critical value for z 0.01.

3. Refer below: Men’s heights are normally distributed with mean 69.0 in. and standard deviation 2.8 in. Women’s heights are normally distributed with mean 63.6 in. and standard deviation 2.5 in.
Use the above information to solve the following question:
If the Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 in.
a. What percentage of adult men can fit through the door without bending?
b. What percentage of adult women can fit through the door without bending?
c. Does the door design with a height of 51.6 in. appear to be adequate? Why didn’t the engineers design a larger door?
d. What doorway height would allow 60% of men to fit without bending?

4. Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all men. (Accommodating 100% of men would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in. Find P99 or the hip breadth for men that separates the smallest 99% from the largest 1%.

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