Adult women's head circumferences are approximately Normally distributed with a mean 56.9 cm and a standard deviation of 1.8 cm. You are manufacturing a new type of helmet for female recruits in the Canadian military and are planning on producing three sizes: small, medium, large. Each size will fit a range of head circumferences. Assume female recruits have similar head circumferences with the general population. a) In order to fit 95% of the recruits, the small size should fit what size head at the smalled, and the large size should fit what size of head at the biggest? b) If medium is to fit at most 60% of recruits, it should fit what head circumference? c) If small fits those with head circumferences between 50 cm and 55 cm, what percent of recruits will need this size? d) If the large size is to fit the biggest 10% of heads, what is the smalled circumference suitable for a large helmet? e) If you decide to make a special production run of a few extra small helmets, suitable for the smallest 2% of recruit circumferences, what circumference will it fit?
Adult women's head circumferences are approximately
a) In order to fit 95% of the recruits, the small size should fit what size head at the smalled, and the large size should fit what size of head at the biggest?
b) If medium is to fit at most 60% of recruits, it should fit what head circumference?
c) If small fits those with head circumferences between 50 cm and 55 cm, what percent of recruits will need this size?
d) If the large size is to fit the biggest 10% of heads, what is the smalled circumference suitable for a large helmet?
e) If you decide to make a special production run of a few extra small helmets, suitable for the smallest 2% of recruit circumferences, what circumference will it fit?
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