Question

# 1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of...

1. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.5 years, and standard deviation of 2 years. The 8% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place.

2. A particular fruit's weights are normally distributed, with a mean of 796 grams and a standard deviation of 13 grams.

The heaviest 7% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Solution :

mean = = 7.5

standard deviation = = 2

Using standard normal table,

P(Z < z) = 8%

P(Z < -1.405) = 0.08

z = -1.405

Using z-score formula,

x = -z * +

x =- 1.405 * 2 + 7.5 = 4.69

shortest lifespan = 4.69 years

2)

Given that,

mean = = 796

standard deviation = = 13

Using standard normal table,

P(Z > z) = 7%

= 1 - P(Z < z) = 0.07

= P(Z < z) = 1 - 0.07

= P(Z < z ) = 0.93

= P(Z < 1.48) = 0.93

z =1.48

Using z-score formula,

x = z * +

x = 1.48* 13+796

x = 815.24

Thank you so much

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