Question

The army reports that a distribution of head circumference among male soldiers is approximately Normal with mean 22.8 inches and standard deviation of 1.1 inches. The army plans on making helmets to fit the middle 98% and will need to make custom helmets for those outside of the range. What heads will not require custom fitted helmets?

A) 20.24, 25.36

B) 20.6, 25

C) 20.26, 25.34

If women's heads are normally distributed with a mean of 22.2 and std deviation of 1.4, what proportion of women can use the ready-made helmets that exist for men? Ready made helmets range from 20.24 to 25.36

A) .985

B) .963

C) .95

D) .907

I can stuck on these pls explain!

Answer 1

Solution :

=> Answer :- Option A) 20.24, 25.36

Given that mean μ = 22.8 , standard deviation σ = 1.1

=> P(z1 < Z < z2) = 0.98

=> z1 = -2.33 , z2 = 2.33

=> X = μ + z1*σ and X = μ + z2*σ

= 22.8 - 2.33*1.1 = 22.8 + 2.33*1.1

= 20.237 = 25.363

= 20.24 (rounded) = 25.36 (rounded)

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Solution :

=> Answer :- Option D) 0.907

Given that mean μ = 22.2 , standard deviation σ = 1.4

=> P(20.24 < x < 25.36) = P((20.24 - 22.2)/1.4 < (x - μ)/σ < (25.36 - 22.2)/1.4)

= P(-1.4 < Z < 2.2571)

= 0.9073