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xxTIMURxx [149]
3 years ago
11

The weight of laboratory mice follows a normal distribution, with a mean of 0.68 ounce and a standard deviation of 0.02 ounce. W

hat percentage of the mice weigh between 0.62 ounce and 0.74 ounce?
A.99.7%
B.95%
C.68%
D.47.5%
E.34%
Mathematics
1 answer:
elena-14-01-66 [18.8K]3 years ago
7 0

Answer:

A.99.7%

Step-by-step explanation:

We are given;

  • Mean of a distribution, μ as 0.68 ounce
  • Standard deviation, σ as 0.02 ounce
  • The range values of X between 0.62 ounce and 0.74 ounce

We are required to calculate the percentage of the weight to be between 0.62 ounce and 0.74 ounce

Step 1: Calculate the Z-score

To get the Z-score we use the formula;

Z-score = (x-μ)/σ

Therefore, when x = 0.62

Then z score = (0.62 - 0.68 ) ÷ 0.02

                     = -3

When, x = 0.74

Then, Z score = (0.74 - 0.68) ÷ 0.02

                       = 3

Step 2:  we use the Z-score table or the empirical rule

Using the Z-score table;

P(-3 < z < 3) = 99.7%.

Therefore; the percentage of mice that weigh between 0.62 ounce and 0.74 ounce is 99.7%.

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Answer:

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Step-by-step explanation:

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4 0
3 years ago
An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 90 and a stan
weqwewe [10]

Answer:

The proportion of children that have an index of at least 110 is 0.0478.

Step-by-step explanation:

The given distribution has a mean of 90 and a standard deviation of 12.

Therefore mean, \mu = 90 and standard deviation, \sigma = 12.

It is given to find the proportion of children having an index of at least 110.

We can take the variable to be analysed to be x = 110.

Therefore we have to find p(x < 110), which is left tailed.

Using the formula for z which is p( Z < \frac{x - \mu}{\sigma}) we get p(Z < \frac{110 - 90}{12} = 1.67).

So we have to find p(Z ≥ 1.67) = 1 - p(Z < 1.67)

Using the Z - table we can calculate p(Z < 1.67)  = 0.9522.

Therefore p(Z ≥ 1.67) = 1 - 0.9522 = 0.0478

Therefore the proportion of children that have an index of at least 110 is 0.0478

8 0
3 years ago
María compró 78 metros de cuerda, ella dividió en 6 partes iguales la cuerda el día martes 8 de mayo ¿Cuántos metros mide cada t
barxatty [35]

Answer:

The length of each piece is 13 m.

Step-by-step explanation:

Maria bought 78 meters of rope, she divided the rope into 6 equal parts on Tuesday, May 8, How many meters is each piece?  

a) Each piece measures 312m

c) Each piece measures 13m

d) each piece mites 92m

b) Each piece measures 9m and 75cm

Total length, L =  78 m

Number of pieces, n = 6

length of each piece,

d = L/n = 78/6 = 13 m

So, the correct option is (c).  

6 0
3 years ago
If 1503 kg of rice was packed in sacks weighing 3 kg each, how many sacks were packed
AURORKA [14]

Answer:

501 sacks

Step-by-step explanation:

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6 0
2 years ago
The formula for the volume of a cone is V =1/3 pi*r^2h. If the radius (r) is doubled and
pishuonlain [190]
V = 1/3* h * r^3 pi
V ' = 1/3* h/3* (2r)^3 pi = h/9 * 8r^3 * pi

V ' / V = (h/9 * 8r^3 * pi)  ÷ ( 1/3* h * r^3 pi ) = (8 * 3)/ 9 = 8 /3


5 0
2 years ago
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