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svetoff
1 month ago
5

A sample of 100 cans of peas showed an average weight of 14 ounces with a standard deviation of 0.7 ounces. If the distribution

is fairly normal, how many cans will weigh over 14.7 ounces?
Mathematics
2 answers:
babunello [11.8K]1 month ago
8 0
This illustrates a normal distribution, with an average weight of 14 ounces and a standard deviation of 0.7 ounces.
14.7 is calculated as 14 + 0.7 = Average + 1 Standard Deviation.
Therefore, the percentage of cans weighing over 14.7 ounces is:
100% - ( 50 % + 34 % ) = 100% - 84% = 16%
This results in 16 out of 100 cans: 16/100 * 100 = 16.
Final answer: 16 cans.
babunello [11.8K]1 month ago
7 0

Answer:

16

Step-by-step explanation:

We know that a sample of 100 cans of peas showed an average weight of 14 ounces with a standard deviation of 0.7 ounces.

Thus, \mu = 14

\sigma = 0.7

Formula: z =\frac{x-\mu}{\sigma}

Given we need to find the number of cans exceeding 14.7 ounces

So, x = 14.7

z =\frac{14.7-14}{0.7}

z =1

Utilizing the z table

P(z>1)=1-P(z<1)=1-0.8413=0.1587

In a sample of 100 cans

Thus, the count of cans weighing over 14.7 ounces = 0.1587\times 100

                                                                            = 15.87

Consequently, the number of cans weighing more than 14.7 ounces is 16.

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