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Answer:
The proportion of sweet cherries that weigh less than 5 ounces is 23.88%.
Step-by-step explanation:
We are given that the weight of sweet cherries is normally distributed with mean μ = 6 ounces and standard deviation σ = 1.4 ounces.
Let X = the weight of sweet cherries
SO, X ~ Normal(μ = 6 ounces , σ = 1.4 ounces)
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 6 ounces
= standard deviation = 1.4 ounces
Now, the proportion of sweet cherries that weigh less than 5 ounces is given by = P(X < 5 ounces)
P(X < 5 ounces) = P( <
) = P(Z < -0.71) = 1 - P(Z
0.71)
= 1 - 0.7612 = <u>0.2388</u>
The above probability is calculated by looking at the value of x = 0.71 from the z table which has an area of 0.7612.