Can you answer the following showing working and formula used.
style="white-space:normal;color:rgb(51,51,51);font-family:sans-serif, Arial, Verdana, 'Trebuchet MS', 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol';background-color:rgb(255,255,255);">The length of a screw manufactured by a company is normally distributed with mean 2.5cm and a standard deviation 0.1cm. Specifications call for the lengths to range from 2.4cm to 2.6 cm.
a, What proportion of parts will be greater than 2.65cm?
b, What length is exceeded by 10% of the parts?
c, What percentage of parts will not meet the specification?
d, If you randomly pick three of those items, what would be the probability that exactly two of them will meet the specification?
e, what value of the standard deviation is required so than less than 7% of screws have a length greater then 2.8cm?
f, Another manufacturer produces the same screws for which 15% of the screws have length less than 1.75cm and 12% of the screws have length higher than 3.2cm. Find the mean and standard deviation of the length of the screw manufactured by the company assuming the length is normally distributed.
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