The weights of tomatos is normally distributed If the middle

The weights of tomatos is normally distributed. If the middle 83% weigh between 2.24 ounces and 5.29 ounces, then what is the mean weight of the tomatoes?

The weights of tomatos is normally distributed. If the middle 95.44% weigh between 4.55 ounces and 9.85 ounces, then what is the standard deviation of the weights?

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Solution

The weights of tomatos is normally distributed. If the middle 83% weigh between 2.24 ounces and 5.29 ounces, then what is the mean weight of the tomatoes?

mean=( lower limit + upper limit)/2 =( 2.24+5.29)/2 =3.765

The weights of tomatos is normally distributed. If the middle 95.44% weigh between 4.55 ounces and 9.85 ounces, then what is the standard deviation of the weights?

Margin of error   = ( upper limit -lower limit)/2

Margin of error = ( 9.85-4.55) /2 = 2.65

middle 95.44% of values with in 2SD limits

Margin of error = 2*sd = 2.65

Sd =2.65/2=1.325