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S, Suppose that the a imount of sodiom per alice of white lerezad geuduced and a

ID: 3309460 • Letter: S

Question

S, Suppose that the a imount of sodiom per alice of white lerezad geuduced and a food atandard deviatiom of 22 prw essing company is nomally distributed with a inem nig a) what ia the pnobalbiliay that a randomuly selected sce wl omn 82 nd 100 mg of sodium? b) What is the likelihood that a randosnly selected slice will 100 mg of sodium? c) What must the amount of sodium (in mg) in a particular slice of ir40% of all slices have more sodium? d) What must the amount of sodium (in mg) in a particular slice of bread be if 2.5% of all slices have more sodium? c) 83% of the slices of bread produced by this food processing company will contain at least how many mg of sodium?

Explanation / Answer

Mean = 110 mg

Standard deviation = 22 mg

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(82 < X < 100) = P(X < 100) - P(X < 82)

= P(Z < (100 - 110)/22) - P(Z < (82 - 110)/22)

= P(Z < -0.455) - P(Z < -1.273)

= 0.3246 - 0.1015

= 0.2231

b) P(at least 100) = P(X > 100)

= 1 - P(X < 100)

= 1 - 0.3246

= 0.6754

c) Let M be the required amount

P(X > M) = 0.4

P(Z < (M - 110)/22) = 0.6

(M - 110)/22 = 0.253

M = 115.57

d) Let the sodium quantity be A

P(X > A) = 0.025

P(X < A) = 0.975

P(Z < (A - 110)/22) = 0.975

(A - 110)/22 = 1.96

A = 153.12

e) Le H be the amount

P(X < H) = 0.83

P(Z < (H - 110)/22) = 0.83

(H - 110)/22 = 128.26 mg