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
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.